Are you pronouncing Caroline rhyming with mine or fine? If so, I think it's close in a sweet way, but not problematic. If you're pronouncing it more like Carolyn, then it feels a little too close to Katharine.
Also, have you thought about nicknames? Does Katharine have a nickname?
With sisters named Clare, Katharine, and Caroline, I'd be inclined to stick with Cs and Ks in the future because it feels so tidily cohesive.
We pronounce it to rhyme with "fine". Katharine goes by her full name or Kat or whatever silly Kat related nickname (Kitty, Kitten, etc) that my husband can come up with. I agree that a 4th daughter would seem to need another C/K name and that makes me nervous as I don't want to be boxed in.
Current favorites - Lucy Caroline and Peter Nathaniel