Is there a cipher that interleaves rounds from other ciphers (with the same block size)? For example, interleaving the rounds of AES/Twofish/Serpent/RC6?
kodlu mentions the interactions of the key schedules; with such a design, I would worry far more about the interaction between the round functions themselves.
A single round of AES, Serpent, Twofish, RC6 has high probability linear and differential characteristics; there's a reason why we have multiple rounds. Now, the round functions within these ciphers are designed so that they play nicely with themselves; that while (say) a single round of AES has high probability characteristics, these high probability characteristics do no apply to multiple rounds. That is, while we can find a high probability characteristic for a single round, we cannot join these high probability characteristics across multiple rounds. This isn't by happenstance, the designers of these ciphers deliberately set things up this way.
This is not necessarily true while you mix-and-match round functions; while we can't find a high-probability characteristic that goes through several AES round functions in succession, there's nothing that says we can't find a characteristic that goes through an AES round function, followed by a Serpent round function, followed by a Twofish round function. I'm not saying there is such a characteristic; I am saying it would appear foolish without doing a whole lot of analysis first.
If you feel an absolute need to do this sort of thing, it would make a lot more sense to keep the round functions from the same cipher together; do a bunch of AES round functions, followed by a bunch of Serpent round functions, followed by a bunch of Twofish round functions. There, we can at least leverage some of the security proofs inherent within the separate ciphers.
I am not aware of any such design.
It would be complex (more complicated than just composing the ciphers, which is not of clear benefit either, by the principle of weakest link) and inefficient since you'd have 3 times as long keylength.
Worse, it would be much much harder to cryptanalyze than straight composition, and thus no one would take it up. You'd need to consider interactions of 3 key schedules, and different design philosophies of the components may introduce unforeseen weaknesses.