The Caitians operate a single Excelsior-A in addition to their Fatherships. It was a trial with using Starfleet designs, that they don't seem to keen to continue with, given their lack of any other units of any class being built.
They did use Starfleet sensor packages in their most recent Fathership design.
They also built a second Excelsior-A and now have two Excelsiors.