diff --git a/src/BlockArraysExtensions/blockedunitrange.jl b/src/BlockArraysExtensions/blockedunitrange.jl
index 2e916729..35779057 100644
--- a/src/BlockArraysExtensions/blockedunitrange.jl
+++ b/src/BlockArraysExtensions/blockedunitrange.jl
@@ -29,10 +29,16 @@ axis(a::AbstractVector) = axes(a, 1)
 function eachblockaxis(a::AbstractVector)
   return map(axis, blocks(a))
 end
+function blockaxistype(a::AbstractVector)
+  return eltype(eachblockaxis(a))
+end
 
 # Take a collection of axes and mortar them
 # into a single blocked axis.
 function mortar_axis(axs)
+  return blockrange(axs)
+end
+function mortar_axis(axs::Vector{<:Base.OneTo{<:Integer}})
   return blockedrange(length.(axs))
 end
 
diff --git a/src/abstractblocksparsearray/abstractblocksparsearray.jl b/src/abstractblocksparsearray/abstractblocksparsearray.jl
index e90e97e0..4cb6b75a 100644
--- a/src/abstractblocksparsearray/abstractblocksparsearray.jl
+++ b/src/abstractblocksparsearray/abstractblocksparsearray.jl
@@ -19,12 +19,12 @@ end
 
 # Specialized in order to fix ambiguity error with `BlockArrays`.
 function Base.getindex(a::AbstractBlockSparseArray{<:Any,N}, I::Vararg{Int,N}) where {N}
-  return @interface BlockSparseArrayInterface() getindex(a, I...)
+  return @interface interface(a) getindex(a, I...)
 end
 
 # Specialized in order to fix ambiguity error with `BlockArrays`.
 function Base.getindex(a::AbstractBlockSparseArray{<:Any,0})
-  return @interface BlockSparseArrayInterface() getindex(a)
+  return @interface interface(a) getindex(a)
 end
 
 ## # Fix ambiguity error with `BlockArrays`.
@@ -53,7 +53,7 @@ end
 
 # Fix ambiguity error.
 function Base.setindex!(a::AbstractBlockSparseArray{<:Any,0}, value)
-  @interface BlockSparseArrayInterface() setindex!(a, value)
+  @interface interface(a) setindex!(a, value)
   return a
 end
 
diff --git a/src/abstractblocksparsearray/broadcast.jl b/src/abstractblocksparsearray/broadcast.jl
index 3527831c..1a9eafc1 100644
--- a/src/abstractblocksparsearray/broadcast.jl
+++ b/src/abstractblocksparsearray/broadcast.jl
@@ -2,7 +2,7 @@ using BlockArrays: AbstractBlockedUnitRange, BlockSlice
 using Base.Broadcast: Broadcast
 
 function Broadcast.BroadcastStyle(arraytype::Type{<:AnyAbstractBlockSparseArray})
-  return BlockSparseArrayStyle{ndims(arraytype)}()
+  return BlockSparseArrayStyle(BroadcastStyle(blocktype(arraytype)))
 end
 
 # Fix ambiguity error with `BlockArrays`.
diff --git a/src/abstractblocksparsearray/map.jl b/src/abstractblocksparsearray/map.jl
index 4dcec66f..494503ac 100644
--- a/src/abstractblocksparsearray/map.jl
+++ b/src/abstractblocksparsearray/map.jl
@@ -111,9 +111,13 @@ function Base.isreal(a::AnyAbstractBlockSparseArray)
   return @interface interface(a) isreal(a)
 end
 
+# Helps with specialization.
 function Base.:*(x::Number, a::AnyAbstractBlockSparseArray)
   return map(Base.Fix1(*, x), a)
 end
 function Base.:*(a::AnyAbstractBlockSparseArray, x::Number)
   return map(Base.Fix2(*, x), a)
 end
+function Base.:/(a::AnyAbstractBlockSparseArray, x::Number)
+  return map(Base.Fix2(/, x), a)
+end
diff --git a/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl b/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
index b72f1e41..73c709e2 100644
--- a/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
+++ b/src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl
@@ -29,8 +29,8 @@ const AnyAbstractBlockSparseVecOrMat{T,N} = Union{
   AnyAbstractBlockSparseVector{T},AnyAbstractBlockSparseMatrix{T}
 }
 
-function DerivableInterfaces.interface(::Type{<:AnyAbstractBlockSparseArray})
-  return BlockSparseArrayInterface()
+function DerivableInterfaces.interface(arrayt::Type{<:AnyAbstractBlockSparseArray})
+  return BlockSparseArrayInterface(interface(blocktype(arrayt)))
 end
 
 # a[1:2, 1:2]
@@ -88,7 +88,7 @@ end
 
 # BlockArrays `AbstractBlockArray` interface
 function BlockArrays.blocks(a::AnyAbstractBlockSparseArray)
-  @interface BlockSparseArrayInterface() blocks(a)
+  @interface interface(a) blocks(a)
 end
 
 # Fix ambiguity error with `BlockArrays`
@@ -230,10 +230,19 @@ function Base.similar(
   return similar(arraytype, eltype(arraytype), axes)
 end
 
+# This circumvents some issues with `TypeParameterAccessors.similartype`.
+# TODO: Fix this poperly in `TypeParameterAccessors.jl`.
+function _similartype(arrayt::Type{<:AbstractArray}, elt::Type, axt::Type{<:Tuple})
+  return Base.promote_op(similar, arrayt, elt, axt)
+end
+function _similartype(arrayt::Type{<:AbstractArray}, axt::Type{<:Tuple})
+  return Base.promote_op(similar, arrayt, axt)
+end
+
 function blocksparse_similar(a, elt::Type, axes::Tuple)
-  return BlockSparseArray{elt,length(axes),similartype(blocktype(a), elt, axes)}(
-    undef, axes
-  )
+  block_axt = Tuple{blockaxistype.(axes)...}
+  blockt = _similartype(blocktype(a), Type{elt}, block_axt)
+  return BlockSparseArray{elt,length(axes),blockt}(undef, axes)
 end
 @interface ::AbstractBlockSparseArrayInterface function Base.similar(
   a::AbstractArray, elt::Type, axes::Tuple{Vararg{Int}}
@@ -275,7 +284,7 @@ function Base.similar(
   elt::Type,
   axes::Tuple{Vararg{AbstractUnitRange{<:Integer}}},
 )
-  return @interface BlockSparseArrayInterface() similar(arraytype, elt, axes)
+  return @interface interface(arraytype) similar(arraytype, elt, axes)
 end
 
 # TODO: Define a `@interface BlockSparseArrayInterface() similar` function.
@@ -302,8 +311,7 @@ function Base.similar(
     AbstractBlockedUnitRange{<:Integer},Vararg{AbstractBlockedUnitRange{<:Integer}}
   },
 )
-  # TODO: Use `@interface interface(a) similar(...)`.
-  return @interface BlockSparseArrayInterface() similar(a, elt, axes)
+  return @interface interface(a) similar(a, elt, axes)
 end
 
 # Fixes ambiguity error with `OffsetArrays`.
@@ -312,8 +320,7 @@ function Base.similar(
   elt::Type,
   axes::Tuple{AbstractUnitRange{<:Integer},Vararg{AbstractUnitRange{<:Integer}}},
 )
-  # TODO: Use `@interface interface(a) similar(...)`.
-  return @interface BlockSparseArrayInterface() similar(a, elt, axes)
+  return @interface interface(a) similar(a, elt, axes)
 end
 
 # Fixes ambiguity error with `BlockArrays`.
@@ -322,8 +329,7 @@ function Base.similar(
   elt::Type,
   axes::Tuple{AbstractBlockedUnitRange{<:Integer},Vararg{AbstractUnitRange{<:Integer}}},
 )
-  # TODO: Use `@interface interface(a) similar(...)`.
-  return @interface BlockSparseArrayInterface() similar(a, elt, axes)
+  return @interface interface(a) similar(a, elt, axes)
 end
 
 # Fixes ambiguity errors with BlockArrays.
@@ -336,16 +342,14 @@ function Base.similar(
     Vararg{AbstractUnitRange{<:Integer}},
   },
 )
-  # TODO: Use `@interface interface(a) similar(...)`.
-  return @interface BlockSparseArrayInterface() similar(a, elt, axes)
+  return @interface interface(a) similar(a, elt, axes)
 end
 
 # Fixes ambiguity error with `StaticArrays`.
 function Base.similar(
   a::AnyAbstractBlockSparseArray, elt::Type, axes::Tuple{Base.OneTo,Vararg{Base.OneTo}}
 )
-  # TODO: Use `@interface interface(a) similar(...)`.
-  return @interface BlockSparseArrayInterface() similar(a, elt, axes)
+  return @interface interface(a) similar(a, elt, axes)
 end
 
 struct BlockType{T} end
diff --git a/src/blocksparsearray/blocksparsearray.jl b/src/blocksparsearray/blocksparsearray.jl
index d92580fe..75a5d304 100644
--- a/src/blocksparsearray/blocksparsearray.jl
+++ b/src/blocksparsearray/blocksparsearray.jl
@@ -173,7 +173,9 @@ end
 function BlockSparseArray{T,N}(
   ::UndefInitializer, axes::Tuple{Vararg{AbstractUnitRange{<:Integer},N}}
 ) where {T,N}
-  return BlockSparseArray{T,N,Array{T,N}}(undef, axes)
+  axt = Tuple{blockaxistype.(axes)...}
+  A = _similartype(Array{T}, axt)
+  return BlockSparseArray{T,N,A}(undef, axes)
 end
 
 function BlockSparseArray{T,N}(
@@ -230,6 +232,20 @@ function BlockSparseArray{T}(
   return BlockSparseArray{T}(undef, axes)
 end
 
+function blocksparsezeros(elt::Type, axes...)
+  return BlockSparseArray{elt}(undef, axes...)
+end
+function blocksparsezeros(::BlockType{A}, axes...) where {A<:AbstractArray}
+  return BlockSparseArray{eltype(A),ndims(A),A}(undef, axes...)
+end
+function blocksparse(d::Dict{<:Block,<:AbstractArray}, axes...)
+  a = blocksparsezeros(BlockType(valtype(d)), axes...)
+  for I in eachindex(d)
+    a[I] = d[I]
+  end
+  return a
+end
+
 # Base `AbstractArray` interface
 Base.axes(a::BlockSparseArray) = a.axes
 
@@ -238,6 +254,10 @@ Base.axes(a::BlockSparseArray) = a.axes
 @interface ::AbstractBlockSparseArrayInterface BlockArrays.blocks(a::BlockSparseArray) =
   a.blocks
 
+function blocktype(arraytype::Type{<:BlockSparseArray{<:Any,<:Any,A}}) where {A}
+  return A
+end
+
 # TODO: Use `TypeParameterAccessors`.
 function blockstype(
   arraytype::Type{<:BlockSparseArray{T,N,A,Blocks}}
diff --git a/src/blocksparsearrayinterface/arraylayouts.jl b/src/blocksparsearrayinterface/arraylayouts.jl
index f1e70c91..a8ac596c 100644
--- a/src/blocksparsearrayinterface/arraylayouts.jl
+++ b/src/blocksparsearrayinterface/arraylayouts.jl
@@ -1,6 +1,6 @@
 using ArrayLayouts: ArrayLayouts, Dot, MatMulMatAdd, MatMulVecAdd, MulAdd
 using BlockArrays: BlockArrays, BlockLayout, muladd!
-using DerivableInterfaces: @interface
+using DerivableInterfaces: DerivableInterfaces, @interface, interface
 using SparseArraysBase: SparseLayout
 using LinearAlgebra: LinearAlgebra, dot, mul!
 
@@ -11,6 +11,10 @@ using LinearAlgebra: LinearAlgebra, dot, mul!
   return a_dest
 end
 
+function DerivableInterfaces.interface(m::MulAdd)
+  return interface(m.A, m.B, m.C)
+end
+
 function ArrayLayouts.materialize!(
   m::MatMulMatAdd{
     <:BlockLayout{<:SparseLayout},
@@ -18,8 +22,7 @@ function ArrayLayouts.materialize!(
     <:BlockLayout{<:SparseLayout},
   },
 )
-  α, a1, a2, β, a_dest = m.α, m.A, m.B, m.β, m.C
-  @interface BlockSparseArrayInterface() muladd!(m.α, m.A, m.B, m.β, m.C)
+  @interface interface(m) muladd!(m.α, m.A, m.B, m.β, m.C)
   return m.C
 end
 function ArrayLayouts.materialize!(
@@ -29,7 +32,7 @@ function ArrayLayouts.materialize!(
     <:BlockLayout{<:SparseLayout},
   },
 )
-  @interface BlockSparseArrayInterface() matmul!(m)
+  @interface interface(m) matmul!(m)
   return m.C
 end
 
@@ -42,5 +45,5 @@ end
 end
 
 function Base.copy(d::Dot{<:BlockLayout{<:SparseLayout},<:BlockLayout{<:SparseLayout}})
-  return @interface BlockSparseArrayInterface() dot(d.A, d.B)
+  return @interface interface(d.A, d.B) dot(d.A, d.B)
 end
diff --git a/src/blocksparsearrayinterface/blocksparsearrayinterface.jl b/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
index 5c1ed5be..1356f949 100644
--- a/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
+++ b/src/blocksparsearrayinterface/blocksparsearrayinterface.jl
@@ -16,7 +16,8 @@ using BlockArrays:
   blocklength,
   blocks,
   findblockindex
-using DerivableInterfaces: DerivableInterfaces, @interface, DefaultArrayInterface, zero!
+using DerivableInterfaces:
+  DerivableInterfaces, @interface, AbstractArrayInterface, DefaultArrayInterface, zero!
 using LinearAlgebra: Adjoint, Transpose
 using SparseArraysBase:
   AbstractSparseArrayInterface,
@@ -104,13 +105,29 @@ blocktype(a::BlockArray) = eltype(blocks(a))
 abstract type AbstractBlockSparseArrayInterface{N} <: AbstractSparseArrayInterface{N} end
 
 # TODO: Also support specifying the `blocktype` along with the `eltype`.
-function Base.similar(::AbstractBlockSparseArrayInterface, T::Type, ax::Tuple)
-  return similar(BlockSparseArray{T}, ax)
+function Base.similar(interface::AbstractBlockSparseArrayInterface, T::Type, ax::Tuple)
+  N = length(ax)
+  block_axt = Tuple{blockaxistype.(ax)...}
+  B = _similartype(blockinterface(interface), Type{T}, block_axt)
+  return similar(BlockSparseArray{T,N,B}, ax)
 end
 
-struct BlockSparseArrayInterface{N} <: AbstractBlockSparseArrayInterface{N} end
+struct BlockSparseArrayInterface{N,B<:AbstractArrayInterface{N}} <:
+       AbstractBlockSparseArrayInterface{N}
+  blockinterface::B
+end
+blockinterface(interface::BlockSparseArrayInterface) = getfield(interface, :blockinterface)
+function BlockSparseArrayInterface{N}(blockinterface::AbstractArrayInterface{N}) where {N}
+  return BlockSparseArrayInterface{N,typeof(blockinterface)}(blockinterface)
+end
+function BlockSparseArrayInterface{N}() where {N}
+  return BlockSparseArrayInterface{N}(DefaultArrayInterface{N}())
+end
 BlockSparseArrayInterface(::Val{N}) where {N} = BlockSparseArrayInterface{N}()
 BlockSparseArrayInterface{M}(::Val{N}) where {M,N} = BlockSparseArrayInterface{N}()
+function BlockSparseArrayInterface{M,B}(::Val{N}) where {M,B<:AbstractArrayInterface{M},N}
+  return BlockSparseArrayInterface{N,B}(B(Val(N)))
+end
 BlockSparseArrayInterface() = BlockSparseArrayInterface{Any}()
 
 @interface ::AbstractBlockSparseArrayInterface function BlockArrays.blocks(a::AbstractArray)
diff --git a/src/blocksparsearrayinterface/broadcast.jl b/src/blocksparsearrayinterface/broadcast.jl
index d8ab5ec8..f3cad907 100644
--- a/src/blocksparsearrayinterface/broadcast.jl
+++ b/src/blocksparsearrayinterface/broadcast.jl
@@ -3,19 +3,28 @@ using GPUArraysCore: @allowscalar
 using MapBroadcast: Mapped
 using DerivableInterfaces: DerivableInterfaces, @interface
 
-abstract type AbstractBlockSparseArrayStyle{N} <: AbstractArrayStyle{N} end
+abstract type AbstractBlockSparseArrayStyle{N,B} <: AbstractArrayStyle{N} end
 
-function DerivableInterfaces.interface(::Type{<:AbstractBlockSparseArrayStyle})
-  return BlockSparseArrayInterface()
+function DerivableInterfaces.interface(
+  ::Type{<:AbstractBlockSparseArrayStyle{N,B}}
+) where {N,B}
+  return BlockSparseArrayInterface(interface(B))
 end
 
-struct BlockSparseArrayStyle{N} <: AbstractBlockSparseArrayStyle{N} end
+struct BlockSparseArrayStyle{N,B<:AbstractArrayStyle{N}} <:
+       AbstractBlockSparseArrayStyle{N,B}
+  blockstyle::B
+end
+function BlockSparseArrayStyle{N}(blockstyle::AbstractArrayStyle{N}) where {N}
+  return BlockSparseArrayStyle{N,typeof(blockstyle)}(blockstyle)
+end
 
 # Define for new sparse array types.
 # function Broadcast.BroadcastStyle(arraytype::Type{<:MyBlockSparseArray})
 #   return BlockSparseArrayStyle{ndims(arraytype)}()
 # end
 
+BlockSparseArrayStyle{N}() where {N} = BlockSparseArrayStyle{N}(DefaultArrayStyle{N}())
 BlockSparseArrayStyle(::Val{N}) where {N} = BlockSparseArrayStyle{N}()
 BlockSparseArrayStyle{M}(::Val{N}) where {M,N} = BlockSparseArrayStyle{N}()
 
diff --git a/src/factorizations/svd.jl b/src/factorizations/svd.jl
index 1f8f4a42..c4871099 100644
--- a/src/factorizations/svd.jl
+++ b/src/factorizations/svd.jl
@@ -20,14 +20,20 @@ function MatrixAlgebraKit.default_svd_algorithm(
   return BlockPermutedDiagonalAlgorithm(alg)
 end
 
+# TODO: Put this in a common location or package,
+# maybe `TypeParameterAccessors.jl`?
+# Also define `imagtype`, `complextype`, etc.
+realtype(a::AbstractArray) = realtype(typeof(a))
+function realtype(A::Type{<:AbstractArray})
+  return Base.promote_op(real, A)
+end
+
+using DiagonalArrays: diagonaltype
 function similar_output(
   ::typeof(svd_compact!), A, S_axes, alg::MatrixAlgebraKit.AbstractAlgorithm
 )
   U = similar(A, axes(A, 1), S_axes[1])
-  T = real(eltype(A))
-  # TODO: this should be replaced with a more general similar function that can handle setting
-  # the blocktype and element type - something like S = similar(A, BlockType(...))
-  S = BlockSparseMatrix{T,Diagonal{T,Vector{T}}}(undef, S_axes)
+  S = similar(A, BlockType(diagonaltype(realtype(blocktype(A)))), S_axes)
   Vt = similar(A, S_axes[2], axes(A, 2))
   return U, S, Vt
 end
@@ -49,9 +55,9 @@ function MatrixAlgebraKit.initialize_output(
   bcolIs = Int.(last.(Tuple.(bIs)))
   for bI in eachblockstoredindex(A)
     row, col = Int.(Tuple(bI))
-    len = minimum(length, (brows[row], bcols[col]))
-    u_axes[col] = brows[row][Base.OneTo(len)]
-    v_axes[col] = bcols[col][Base.OneTo(len)]
+    b = argmin(length, (brows[row], bcols[col]))
+    u_axes[col] = b
+    v_axes[col] = b
   end
 
   # fill in values for blocks that aren't present, pairing them in order of occurence