  If $A\otimes _{R, \sigma }V$ and $A\otimes _{P, \nu }W$ are two Brzezi\'nski
crossed products and $Q:W\otimes V\rightarrow V\otimes W$ is a linear map
satisfying certain properties, we construct a Brzezi\'{n}ski crossed product
$A\otimes _{S, \theta }(V\otimes W)$. This construction contains as a
particular case the iterated twisted tensor product of algebras.
