I play none of those, but if you already like the KID, you may want to check out Leningrad Dutch. It's very similar in a lot of ways to KID, kind of a hybrid system. Imagine if you didn't have to waste time with Ne8, f5, Nf6, but had f5 played already. That's what Leningrad tries to do, at a simplistic level.
If you play Nimzo, you should also be able to play QID and Bogo-Indian from what I understand, as you really need to be able to play whichever is going to be better depending on what white does in response to Nf6, e6.
I currently play the KID as Black against 1. d4. I am looking to learn a second defense to use.
I am trying to decide between the Slav, Nimzo, and QID. So far I'm leaning towards the Slav, but am interested in the opinions of anyone who plays any of those openings.
Thoughts?