To use equines again, most equine species can hybridize. In particular, zebras can be crossed either with horses or donkeys to produce a hybrid “zebrule” (some sources will tell you this is only a term for a specific cross). One species of zebra has 44 chromosomes to the horses 64, but they can still hybridize.
The chromosome count apparently doesn’t much matter for the genes to cooperate in building an organism, as long as the instructions aren’t radically different, ie. if they are closely related species. Packaging into chromosomes would seem to be chiefly a mechanism to allow meiosis to take place, and here, the hybrid is out of luck - it has some intermediate number of chromosomes (mules have 63, intermediate between the horse’s 64 and the donkey’s 62), many of which are unpaired, meaning that the process of meiosis produces a gamete with a lot of missing information.
I’m using the mules because I dug up some stuff on the nature of mules for another thread sometime back, and because they’re probably the most familiar case of hybridization in mammals:
For any “deeper” explanation on the mechanisms involved, I’m out of MY depth. Wait for a biologist.