Loka is a 4-player chess variant that had a successful Kickstarter campaign last year.
The game features both a fantasy-styled chess set that can be used for traditional chess, as well as a variant rule system built around a point-based army building system, and dice for resolving captures.
AncientChess.Com posted an excellent, generally positive overview of how the variant play works:
https://www.youtube.com/watch?v=LhbutaoBbh0