In Europe in the modern era, the trend is more in the other direction: as society gains more respect for both men and women's choice of sexual self-determination, instead of being fixated on traditional opposite-sex, pair-courtship rituals, polyamorous relationships are becoming more accepted. They were once strongly disapproved of and even illegalized, but are now increasingly being seen as a legitimate personal choice. On the activist side, many (most?) LGBTQ organizations also include poly activists, especially the organizations which have a more left-wing flavor.

I think the more likely path than legal polygamy, though, is to expand a more flexible set of legal arrangements for families, as a replacement for traditional marriage being the legal framework. The fact that a huge proportion of couples here (Denmark) no longer get married is already forcing that for another reason. Since many families which otherwise look traditional — long-term cohabitation of an opposite-sex couple, jointly raising children of which they're parents, etc. — don't get married, marriage as the organizing principle of families is becoming less relevant, so the law already has to start handling things differently.