Lots? Just quit so can't check, but there were places in NGC 7822 where I had an ostensibly 3 or 4 star system from the galaxy map, jumped in and discovered that most of those actually had several stars (and we're talking G/K/F, not Dwarves that barely count as stars) orbiting them.
4 CYGNI with 25 Stellar Bodies is the current entry in the Book of Records.
According the the record book 25 stellar bodies in one system is the highest (the aforementioned 4 Cygni). Of course not all report to this book but many enough: