A christian man(or woman I suppose, but in this example a man) could not consistently be a polygamist unless he at the very least…
- Had some very good reason unrelated to lust to justify marrying another woman(otherwise it would be founded by adultery).
- His wife or all of his wives supported him marrying another woman. A jealous or uncertain wife would have the right to put a stop to it, even if we misguidedly believe that jealousy is a dysfunctional, immature, or ungodly emotion.
- He was able to be a good husband to each of them and did not treat them with unfair partiality.
It is very hard to imagine any would-be polygamist meeting those conditions and that is generously assuming that it is even permitted by God to marry more than one person at once, which is questionable.
I have thought about whether there might be exceptional cases where a christian could be legitimately married to more than one woman without being at odds with scripture. I think the strongest case would be for a person that had already married multiple women(and each consented to each marriage) before they became christian. That is a dilemma for those of us that only believe in monogamy, but allowing for that exception would not mean that it is always legitimate. And there are very few if any situations where it would be ideal.