It's more that this other creature could fit in as a different one. In the case of that kumi-whateverjapanesething it would be listed as an Animelious, whereas the cockatrice would be listed as a Dracoavian. You do not just come up with species on the fly... use what you have provided for you. I'd like to prevent redundant species, and the form and powers of each individual species is very varied. We can have metal phoenixes, fox-based animelious with more than one tail (seems to be popular for some reason), gryphons who can't fly but instead can freely move under the ground or something, and, if all that fails, we even have chimeras, which are even more varied in their appearance.
Got four animals that you need your character to be? Well, put them in the blender and call it a chimera.