There is a possibility of adding support for jumbo branches to qp tries. Jumbo branches would have more than 16 twigs (sub-tries).
The flag bits can currently take values 0,1,2, so 3 is available to mark a jumbo branch; as suggested by the flag meanings it would test a whole byte at a time instead of one nibble at a time. Perhaps the bitmap field could be used to choose from multiple branch types, in the style of adaptive radix trees. https://github.com/armon/libart
The key question is how to decide when to coalesce two layers of qp trie into a jumbo branch. A simple option is to coalesce when the upper nibble passes some density threshold. This would work OK for almost-binary keys. However for common ASCII keys, the upper nibble will usually have four or maybe five possible values. In this case the upper nibble alone does not provide a clear signal of the density of the byte, so there is too much risk of wasting time trying to find one.
Perhaps it would be reasonable to sacrifice lexicographic ordering by testing lower nibbles before upper nibbles. Then it is quite likely that a dense byte will fill or nearly fill its first branch. But if it is OK to sacrifice lexicographic ordering, we might as well use a HAMT instead.