If you're the singer and not one of the lead players, I think your problem will be getting the instrumentalists focused enough to remember what new melody they're supposed to play.

It wasn't until I started playing more lead (I sing also) that I recognized that you seem to get into another part of your brain when producing melody, and it really takes some concentration to shift gears. I suspect that's why the Irish session tunes seem to have traditional "sets" that meld easily and are learned almost as one long tune. If you have more than one lead instrument, perhaps one could "lay out" for a few bars in preparation for getting the next tune started. It's not going to be easy, but it should be worth it.