diff --git a/base/broadcast.jl b/base/broadcast.jl
index 6e2809daa2a48..e07ccab2443bc 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -162,6 +162,32 @@ BroadcastStyle(a::AbstractArrayStyle{N}, ::DefaultArrayStyle{N}) where N = a
 BroadcastStyle(a::AbstractArrayStyle{M}, ::DefaultArrayStyle{N}) where {M,N} =
     typeof(a)(_max(Val(M),Val(N)))
 
+# FIXME
+# The following definitions are necessary to limit SparseArray broadcasting to "plain Arrays"
+# (see https://github.com/JuliaLang/julia/pull/23939#pullrequestreview-72075382).
+# They should be deleted once the sparse broadcast infrastucture is capable of handling
+# arbitrary AbstractArrays.
+struct VectorStyle <: AbstractArrayStyle{1} end
+struct MatrixStyle <: AbstractArrayStyle{2} end
+const VMStyle = Union{VectorStyle,MatrixStyle}
+# These lose to DefaultArrayStyle
+VectorStyle(::Val{N}) where N = DefaultArrayStyle{N}()
+MatrixStyle(::Val{N}) where N = DefaultArrayStyle{N}()
+
+BroadcastStyle(::Type{<:Vector}) = VectorStyle()
+BroadcastStyle(::Type{<:Matrix}) = MatrixStyle()
+
+BroadcastStyle(::MatrixStyle, ::VectorStyle) = MatrixStyle()
+BroadcastStyle(a::AbstractArrayStyle{Any}, ::VectorStyle) = a
+BroadcastStyle(a::AbstractArrayStyle{Any}, ::MatrixStyle) = a
+BroadcastStyle(a::AbstractArrayStyle{N}, ::VectorStyle) where N = typeof(a)(_max(Val(N), Val(1)))
+BroadcastStyle(a::AbstractArrayStyle{N}, ::MatrixStyle) where N = typeof(a)(_max(Val(N), Val(2)))
+BroadcastStyle(::VectorStyle, ::DefaultArrayStyle{N}) where N = DefaultArrayStyle(_max(Val(N), Val(1)))
+BroadcastStyle(::MatrixStyle, ::DefaultArrayStyle{N}) where N = DefaultArrayStyle(_max(Val(N), Val(2)))
+# to avoid the VectorStyle(::Val) constructor we also need the following
+BroadcastStyle(::VectorStyle, ::MatrixStyle) = MatrixStyle()
+# end FIXME
+
 ## Allocating the output container
 """
     broadcast_similar(f, ::BroadcastStyle, ::Type{ElType}, inds, As...)
@@ -181,6 +207,17 @@ broadcast_similar(f, ::ArrayConflict, ::Type{ElType}, inds::Indices, As...) wher
 broadcast_similar(f, ::ArrayConflict, ::Type{Bool}, inds::Indices, As...) =
     similar(BitArray, inds)
 
+# FIXME: delete when we get rid of VectorStyle and MatrixStyle
+broadcast_similar(f, ::VectorStyle, ::Type{ElType}, inds::Indices{1}, As...) where ElType =
+    similar(Vector{ElType}, inds)
+broadcast_similar(f, ::MatrixStyle, ::Type{ElType}, inds::Indices{2}, As...) where ElType =
+    similar(Matrix{ElType}, inds)
+broadcast_similar(f, ::VectorStyle, ::Type{Bool}, inds::Indices{1}, As...) =
+    similar(BitArray, inds)
+broadcast_similar(f, ::MatrixStyle, ::Type{Bool}, inds::Indices{2}, As...) =
+    similar(BitArray, inds)
+# end FIXME
+
 ## Computing the result's indices. Most types probably won't need to specialize this.
 broadcast_indices() = ()
 broadcast_indices(::Type{T}) where T = ()
@@ -582,7 +619,7 @@ Nullable{Complex{Float64}}()
     broadcast(f, s, combine_eltypes(f, A, Bs...), combine_indices(A, Bs...),
               A, Bs...)
 
-const NonleafHandlingTypes = Union{DefaultArrayStyle,ArrayConflict}
+const NonleafHandlingTypes = Union{DefaultArrayStyle,ArrayConflict,VectorStyle,MatrixStyle}
 
 @inline function broadcast(f, s::NonleafHandlingTypes, ::Type{ElType}, inds::Indices, As...) where ElType
     if !Base._isleaftype(ElType)
diff --git a/base/sparse/higherorderfns.jl b/base/sparse/higherorderfns.jl
index 1c551fe446aba..447d247746838 100644
--- a/base/sparse/higherorderfns.jl
+++ b/base/sparse/higherorderfns.jl
@@ -989,9 +989,18 @@ PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
 Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
 Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
 
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
+# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
+# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
+# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
+# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
+BroadcastStyle(::Type{<:Base.RowVector{T,<:Vector}}) where T = Broadcast.MatrixStyle() # RowVector not yet defined when broadcast.jl loaded
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
+    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(1)))
+Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
+    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(2)))
+# end FIXME
 
 broadcast(f, ::PromoteToSparse, ::Void, ::Void, As::Vararg{Any,N}) where {N} =
     broadcast(f, map(_sparsifystructured, As)...)