I could see that in certain situations, even if the polygomous relationship is illegal, it would be wrong not to recognize it. For example, a child that needs medical benefits, a wife that is attempting to claim insurance,etc.
I could see something like this:
1. Prohibit the contracting of a polygamous marriage in Canada. If I want to take a second wife, then I'd have to fly her and myself over to a jurisdiction abroad that would allow us to legally contract such a marriage.
2. Require marriage contracts in Canada must include a monogamy clause. Since it would be a contract, this would mean that even Muslim states might refuse to allow a person who's already under such a contract to then contract a marriage with a second person without any present wife agreeing to revise the original contract. This would mean that a man under such a contract might need to bring any present wife with him to have her agree to revise the original contract abroad so as to allow him to take a second wife. Consequently, he could not take a second wife without his first wife's consent. Even if he finds a jurisdiction that's willing to marry him, his first wife could then sue him back in Canada for having broken the contract.
3. Allow family-marriage contracts. This would mean that a woman who wants to make it more difficult for her husband to take a second wife later could have her husband-to-be sign a family-marriage contract whereby his and her living parents would sign to give their consent to a monogamous-marriage contract that could be revised even abroad only with the consent of both spouses and their living parents. This would mean that a man under such a contract would need to fly not only himself, his intended wife-to-be, and his first wife to a jurisdiction that allows the contracting of a polygamous marriage, but would have to fly all of his and her living parents there too so that they could revise the contract.
None of this would prevent a man from divorcing his first wife to marry a second, but it would make it far more difficult for him to take a second wife without his first wife's consent. And in the case of a family-marriage contract, it would even be difficult for him to coerce his wife into revising a monogamous marriage contract wince he'd need the signature of his and her living parents to revise it too.