We establish a tensor product formula for bimodules over maximal abelian self-adjoint algebras and their supports. We use this formula to show that if A is the tensor product of finitely many continuous nest algebras, B is a CSL algebra and A and B have the same normaliser semigroup then either A = B or A * = B. We show that the result does not hold without the assumption that the nests be continuous, answering in the negative a question previously raised in the literature.