No, there are thousands of cichlids from all different types of water and environments on 4 separate continents and many of them can't even live in the same water. Others just can't live together. Firemouth cichlids are great fish and relatively easy to breed. just now. Report Abuse. Yes different kinds of cichlids can live together but not those ones. The firemouth and the severum is fine I would leave out the convict and Zebra cichlid.