The techniques exist to create artificial life, sentient or no. Only the kenaki have the knowledge available to create viable races, a process which takes hundreds of years to complete.
Creating a unique creature is a bit simpler. A knowledgeable, specialized mage could piece together two or more creatures to create a new being in a matter of weeks or months, with the added complexity of wholey unique attributes lengthening the time spent in research and creation.
For example, it's currently popular for the upper class to commission pets combining various small animals, such as mice and sparrows. The creation of a mouse-sparrow involves either the death of both, in which case the resultant creature would then be reanimated with a new spirit, or by killing one and combining the material with the living other. This second process is much simpler, but cannot produce a creature which behaves any differently than the original being. A mouse given sparrow wings will still behave like a mouse, but a mouse-sparrow with a combined brain will be able to tunnel and fly. It's possible to alter the brain of a living subject, so that modifications become functional, but this is apparently more complicated than the other method, and so it's reserved for modifications made directly to clients. The exact process is beyond me. The art requires devotion.
Of course, it's possible to give a person, say, wings, if they have the money for it. Provided their death and reanimation isn't involved, people with magical modifications retain their status. The cost involved makes a few specific modifications stylish and desirable. Tail and ear modifications are gaining in popularity, and unusual or changing eye or hair colors have been common in the upper class for centuries.
I have my hair modified fairly often. It burns a little, but I can't say anything else about the experience. For about fifty kibik, your hair can be whatever color you like, with little trouble.
My older brother had horns for a few years, and it cost him more to have them removed than it did to have them done. More complex modifications are possible. Conceivably, someone could even change their appearance to that of another race, but such extremes are considered tasteless and suspicious, at best.