Ceremorphosis

Ceremorphosis occurs when an illithid tadpole reaches maturity and is inserted into the brain of another humanoid being - usually a human. The tadpole eats away the victim's gray matter and essentially becomes the brain, erasing all of the subject's personality and memory, but leaving the physical body alive and under the tadpole's control. After this "morphological transformations" occur and a new illithid is created.

Half-Illithids
If this is done with a non-human, the result is technically a "half-illithid". They do, however, still possess most of the powers of a regular illithid.