Three men had their relationship officially recognized in Medellin:
It’s not exactly a marriage, but a legal recognition of their status as a family, with inheritance rights :
This legal status is apparently called “trieja”, according to a French article, but I couldn’t find more infos about it.
What I find in Spanish is confusing. On one hand, the articles speak of inheritance law and indicates they have made paperwork making them a three-sided tontine; on the other, the Colombian article indicates that “while polygamy is illegal in Colombia, polyamorous unions are legal as of last month” (which smells to me of the same language-dancing as “legal unions”). The Colombian article also points out that they used to be four: the fourth died recently and the three survivors have been able to obtain their shared widowhood pension.
I expect that Colombia already had the shared widowhood pension process for the case of a man and multiple women, as well as the possibility of making a tontine will. This appears to be an extension of both, but which other rights are included in these “polyamorous unions” is not spelled out in the article.