Assume we are dealing with a society similarly advanced to our own but thanks to finding some data-stores of advanced technology are far more capable at genetic engineering.
With that extra genetic engineering knowledge they have made various demi-human races: cat-human, bird/flying-human, amphibious human etc. These demi-humans fill various roles in society but are treated fairly poorly, as lower caste/disposable slaves.
There are also various subspecies of each of the demi-humans which are denoted by their different features. For example among the cat-human their are different fur & hair length/colour, ear size & shape, nocturnal nature, carnivore/omnivore etc.
Assume that cross breeding is possible and that we can also ignore unusual/useless cross breeds (aquatic human with wings).
How realistic is it for the results of crossbreeding to have a mix of complete features from both species? For example, the cat/bird/human has wings, a cat's tail and human eyes.
How likely are genetic accidents? For example, the cat/bird/human has half formed non-functional wings, a vestigial tail and mismatched eyes.
Keep in mind for these questions that this society has access to advanced genetic engineering. They could attempt to make it so crossbreeding will function as successfully as possible. However, the vast majority of these crossbreeds are slaves/low caste members and could not afford expensive treatments for every child.