diff --git a/src/linalg.jl b/src/linalg.jl
index 3f34e94a..a2f07b22 100644
--- a/src/linalg.jl
+++ b/src/linalg.jl
@@ -1301,6 +1301,13 @@ const _Triangular_SparseKronArrays = UpperOrLowerTriangular{<:Any,<:_SparseKronA
 const _Annotated_SparseKronArrays = Union{_Triangular_SparseKronArrays, _Symmetric_SparseKronArrays, _Hermitian_SparseKronArrays}
 const _SparseKronGroup = Union{_SparseKronArrays, _Annotated_SparseKronArrays}
 
+const _SpecialArrays = Union{Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal}
+const _Symmetric_DenseArrays{T,A<:Matrix} = Symmetric{T,A}
+const _Hermitian_DenseArrays{T,A<:Matrix} = Hermitian{T,A}
+const _Triangular_DenseArrays{T,A<:Matrix} = UpperOrLowerTriangular{<:Any,A} # AbstractTriangular{T,A}
+const _Annotated_DenseArrays = Union{_SpecialArrays, _Triangular_DenseArrays, _Symmetric_DenseArrays, _Hermitian_DenseArrays}
+const _DenseConcatGroup = Union{Number, Vector, Adjoint{<:Any,<:Vector}, Transpose{<:Any,<:Vector}, Matrix, _Annotated_DenseArrays}
+
 @inline function kron!(C::SparseMatrixCSC, A::AbstractSparseMatrixCSC, B::AbstractSparseMatrixCSC)
     mA, nA = size(A); mB, nB = size(B)
     mC, nC = mA*mB, nA*nB
diff --git a/src/sparsevector.jl b/src/sparsevector.jl
index 67c5293c..6ee35828 100644
--- a/src/sparsevector.jl
+++ b/src/sparsevector.jl
@@ -4,8 +4,7 @@
 
 import Base: sort!, findall, copy!
 import LinearAlgebra: promote_to_array_type, promote_to_arrays_
-
-using LinearAlgebra: adj_or_trans, _SpecialArrays, _DenseConcatGroup
+using LinearAlgebra: adj_or_trans
 
 ### The SparseVector
 
@@ -1176,24 +1175,10 @@ function _absspvec_vcat(X::AbstractSparseVector{Tv,Ti}...) where {Tv,Ti}
     SparseVector(len, rnzind, rnzval)
 end
 
-hcat(Xin::Union{Vector, AbstractSparseVector}...) = hcat(map(sparse, Xin)...)
-vcat(Xin::Union{Vector, AbstractSparseVector}...) = vcat(map(sparse, Xin)...)
-
 ### Concatenation of un/annotated sparse/special/dense vectors/matrices
-
-const _SparseArrays = Union{AbstractSparseVector,
-                            AbstractSparseMatrixCSC,
-                            Adjoint{<:Any,<:AbstractSparseVector},
-                            Transpose{<:Any,<:AbstractSparseVector}}
-const _SparseConcatArrays = Union{_SpecialArrays, _SparseArrays}
-
-const _Symmetric_SparseConcatArrays = Symmetric{<:Any,<:_SparseConcatArrays}
-const _Hermitian_SparseConcatArrays = Hermitian{<:Any,<:_SparseConcatArrays}
-const _Triangular_SparseConcatArrays = UpperOrLowerTriangular{<:Any,<:_SparseConcatArrays}
-const _Annotated_SparseConcatArrays = Union{_Triangular_SparseConcatArrays, _Symmetric_SparseConcatArrays, _Hermitian_SparseConcatArrays}
-# It's important that _SparseConcatGroup is a larger union than _DenseConcatGroup to make
-# sparse cat-methods less specific and to kick in only if there is some sparse array present
-const _SparseConcatGroup = Union{_DenseConcatGroup, _SparseConcatArrays, _Annotated_SparseConcatArrays}
+# by type-pirating and subverting the Base.cat design by making these a subtype of the normal methods for it
+# and re-defining all of it here. See https://github.com/JuliaLang/julia/issues/2326
+# for what would have been a more principled way of doing this.
 
 # Concatenations involving un/annotated sparse/special matrices/vectors should yield sparse arrays
 
@@ -1205,23 +1190,55 @@ _sparse(A) = _makesparse(A)
 _makesparse(x::Number) = x
 _makesparse(x::AbstractVector) = convert(SparseVector, issparse(x) ? x : sparse(x))::SparseVector
 _makesparse(x::AbstractMatrix) = convert(SparseMatrixCSC, issparse(x) ? x : sparse(x))::SparseMatrixCSC
+anysparse() = false
+anysparse(X) = X isa AbstractArray && issparse(X)
+anysparse(X, Xs...) = anysparse(X) || anysparse(Xs...)
+
+function hcat(X::Union{Vector, AbstractSparseVector}...)
+    if anysparse(X...)
+        X = map(sparse, X)
+    end
+    return cat(X...; dims=Val(2))
+end
+function vcat(X::Union{Vector, AbstractSparseVector}...)
+    if anysparse(X...)
+        X = map(sparse, X)
+    end
+    return cat(X...; dims=Val(1))
+end
+
+# type-pirate the Base.cat design by making this a subtype of the existing method for it
+# in future versions of Julia (v1.10+), in which https://github.com/JuliaLang/julia/issues/2326 is not fixed yet, the <:Number constraint could be relaxed
+# but see also https://github.com/JuliaSparse/SparseArrays.jl/issues/71
+const _SparseConcatGroup = Union{AbstractVecOrMat{<:Number},Number}
 
 # `@constprop :aggressive` allows `dims` to be propagated as constant improving return type inference
-Base.@constprop :aggressive function Base._cat(dims, Xin::_SparseConcatGroup...)
-    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
-    T = promote_eltype(Xin...)
+Base.@constprop :aggressive function Base._cat(dims, X::_SparseConcatGroup...)
+    T = promote_eltype(X...)
+    if anysparse(X...)
+        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+    end
     return Base._cat_t(dims, T, X...)
 end
-function hcat(Xin::_SparseConcatGroup...)
-    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
+function hcat(X::_SparseConcatGroup...)
+    if anysparse(X...)
+        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+    end
     return cat(X..., dims=Val(2))
 end
-function vcat(Xin::_SparseConcatGroup...)
-    X = (_sparse(first(Xin)), map(_makesparse, Base.tail(Xin))...)
+function vcat(X::_SparseConcatGroup...)
+    if anysparse(X...)
+        X = (_sparse(first(X)), map(_makesparse, Base.tail(X))...)
+    end
     return cat(X..., dims=Val(1))
 end
-hvcat(rows::Tuple{Vararg{Int}}, X::_SparseConcatGroup...) =
-    vcat(_hvcat_rows(rows, X...)...)
+function hvcat(rows::Tuple{Vararg{Int}}, X::_SparseConcatGroup...)
+    if anysparse(X...)
+        vcat(_hvcat_rows(rows, X...)...)
+    else
+        Base.typed_hvcat(promote_eltypeof(X...), rows, X...)
+    end
+end
 function _hvcat_rows((row1, rows...)::Tuple{Vararg{Int}}, X::_SparseConcatGroup...)
     if row1 ≤ 0
         throw(ArgumentError("length of block row must be positive, got $row1"))
@@ -1238,7 +1255,7 @@ end
 _hvcat_rows(::Tuple{}, X::_SparseConcatGroup...) = ()
 
 # make sure UniformScaling objects are converted to sparse matrices for concatenation
-promote_to_array_type(A::Tuple{Vararg{Union{_SparseConcatGroup,UniformScaling}}}) = SparseMatrixCSC
+promote_to_array_type(A::Tuple{Vararg{Union{_SparseConcatGroup,UniformScaling}}}) = anysparse(A...) ? SparseMatrixCSC : Matrix
 promote_to_arrays_(n::Int, ::Type{SparseMatrixCSC}, J::UniformScaling) = sparse(J, n, n)
 
 """