They are all loners.
Muse is the Breakfast Club!
Well, the second years have been a trio since they were children and all of them pretty well-liked by their classmates. Same for Hanayo and Rin. Those five are all pretty well adjusted without any particularly dark backstory.
When it comes down to it, the only one who seems to really enjoy solitude, although she also likes being with her friends, is Maki. Especially if she's got a piano to keep her company.