I think Kate stands alone just fine. I prefer it as a nickname (DD is Katherine nn Kate) but that is just me. With Elizabeth I think people will assume Kate is a nn, but they don't clash as a sibset.
If Katherine and Kathleen are out, I suppose you can try Katelyn (though, I strongly prefer the traditional spelling Caitlin which doesn't lend itself well to the nn Kate). I think Katrina is really pretty and don't think the hurricane has ruined the name. Others... hmmm.. Katerina? Mary Kate?