diff --git a/NEWS.md b/NEWS.md
index cb1ae62f9..e17247191 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -18,6 +18,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Fixed
 
 - Fixed issue where `FineToCoarseField` would not work for vector-valued fields. Since PR[#970](https://github.com/gridap/Gridap.jl/pull/970).
+- Fixed issue where `BlockSparseMatrixAssembler` would not work correctly when permuting variables. Since PR[#971](https://github.com/gridap/Gridap.jl/pull/971).
 
 ## [0.17.21] - 2023-12-04
 
diff --git a/src/MultiField/BlockSparseMatrixAssemblers.jl b/src/MultiField/BlockSparseMatrixAssemblers.jl
index b4a336d74..b8a6e2ae2 100644
--- a/src/MultiField/BlockSparseMatrixAssemblers.jl
+++ b/src/MultiField/BlockSparseMatrixAssemblers.jl
@@ -36,17 +36,20 @@ function FESpaces.get_vector_builder(a::BlockSparseMatrixAssembler{NB,NV}) where
   return expand_blocks(a,builders)
 end
 
-expand_blocks(::BlockSparseMatrixAssembler{NB,NB},blocks::MatrixBlock) where NB = blocks
-expand_blocks(::BlockSparseMatrixAssembler{NB,NB},blocks::VectorBlock) where NB = blocks
-
-function expand_blocks(a::BlockSparseMatrixAssembler{NB,NV},blocks::MatrixBlock) where {NB,NV}
+function expand_blocks(a::BlockSparseMatrixAssembler{NB,NV,SB,P},blocks::MatrixBlock) where {NB,NV,SB,P}
+  if (NB == NV) && all(x -> x[1] == x[2], enumerate(P))
+    return blocks
+  end
   block_map = get_block_map(a)
-  ArrayBlockView(blocks,block_map)
+  return ArrayBlockView(blocks,block_map)
 end
 
-function expand_blocks(a::BlockSparseMatrixAssembler{NB,NV},blocks::VectorBlock) where {NB,NV}
+function expand_blocks(a::BlockSparseMatrixAssembler{NB,NV,SB,P},blocks::VectorBlock) where {NB,NV,SB,P}
+  if (NB == NV) && all(x -> x[1] == x[2], enumerate(P))
+    return blocks
+  end
   block_map = map(idx -> CartesianIndex(idx[1]), diag(get_block_map(a)))
-  ArrayBlockView(blocks,block_map)
+  return ArrayBlockView(blocks,block_map)
 end
 
 function get_block_ranges(NB::Integer,SB,P)