========================================================The passive construction in 'I had my wallet stolen' is obviously irrelevant: no-one planned anything for Saturday against my will or without my knowledge. The causative 'I had the house painted' is closer: it means I got someone else to paint the house for me. But this is still unlikely here: I probably didn't get someone to plan something for Saturday for me. (My secretary, perhaps?) Probably I planned it myself. Another way of saying it is: I planned something for Saturday.
Then, after I had done that, we can say that I had something planned for Saturday. This 'had' is not causative, but possessive: it says what I had.
I have to admit I'm still not 100% convinced my earlier analysis is right. It does feel as if the 'planned' phrase could be a separate complement in the verb phrase. But I think I'm probably right, unless someone can produce better evidence that the two parts can be separated.