I make my own M&P, and I'm only guessing yours is purchased, so my experience might be different from yours. When I tried using my M&P with my CP, two problems were consistently observed:
Remained separate from the CP layers - that is, even after months, it was fairly easy to pull the M&P top/bottom layer away from the CP.
The CP was brittle where it bordered the M&P layers, but only a thin line right along the layer border.
I never experimented to figure out why, but suspected it was due to 1. The different "hardness" of the M&P and CP, and 2. The heat of the M&P (my notes say avg of 169F by the time M&P's fully melted). I'm guessing it's primarily the heat of the M&P since I don't see these two problems as much when using M&P with HP, though they do still happen - at least to me, LOL. I should say that when I use M&P to encase CP "figurines", like stars for instance, I've had no problems, even as the soap is used down to the CP areas.