If you just want to do some longer rides, try it out with what you've got now. Riding long-distance on a fixed gear is a fun challenge.

That being said, I think what you ultimately want is two bikes (and I'm not one of those N+1 pushers, normally). Versatile bikes are cool, and the Cross Check is cool, but converting between fixed and geared is a decent amount of work and probably not something you want to do on a regular basis unless you simply don't have room for an additional bike. Personally, I like the variety of riding both fixed and geared bikes.