Considering double casting, you'd be playing both Kate and Lucy.
I don't think I could play anyone except Brian. Princeton/Rod are just a little too high for me, due to the high Gs, and while Trekkie is within my range, Nicky (who he often doubles with) is most certainly not.
I'd be able to play Rod pretty well (I have the voice down) but if we're going by the double casting precedent in the original, yeah, there's no way I can hit all of Princeton's notes without sounding like Rod at some points.
The original Princeton cheated at one point, in "Purpose." The sheet music designates the "I'm gonna find my purpose yeah" thing as being a string of high Gs. He didn't do that.
Incidentally, Richard Walters (guy who puts together "The Singer's Musical Theatre Anthology," which is a fantastic series you should all own) seems to think that Princeton/Rod is a baritone.