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