If I'm understanding your comment right, you mean that the underlying cuckoo hash table can only use 2 buckets per item, right? We actually generalized this, but only in Bin's thesis:

https://www.cs.cmu.edu/~binfan/thesis/thesis_ss.pdf

See section 4.5. It was a bit more computationally expensive, so we didn't push forward with it in our implementation, as "2,4" cuckoo hash tables (2 hash functions to identify buckets, 4 associative elements) performed so well already.