Typically, programs are "on to" students who are looking for a back door way into a clinical program, and therefore have policies to prohibit such transfers. I wouldn't go so far as to say that it would never happen, but it would have to be a very unique circumstance.
Further, let's say you are 2 years into a social psych degree, and switch into clinical... With the exception of having taken stats, you would essentially be entering the clinical program as a first year student. You would have to make up a lot of required coursework and practicum time.
Some programs admit that it is theoretically possible. But my understanding is that it is very difficult. If you search hard enough, or if you recall, there is always some discussion about this come application time, or come decision time. Invariably someone will want to know if it is a better idea to accept a more desireable school's offer for acceptance ot their general PhD program with the hope of transferring in to the clinical track at a later date vs. taking another clinical offer. In my opinion, based on limited expereince, this is a gamble that wouldn't be worth it. Although it is theoretically possible.