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.
Same in Portugal. People I know are already doing alternative celebrations to regular marriage, influenced in part by the cost - since marriage celebrations are expected to have certain elements (catering, dresses, etc) which these celebrations do without.
"De facto unions" have existed (for both hetero and homosexual partners) for more than ten years already, and have many of the same rights as married couples, including inheritance, refusal do testify in court, etc.
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.