Never heard of anyone having a problem with loading S&B or Fiocchi in their P-32 magazines. I take it by "new to me", you picked-up this P-32 used? Does the magazine have a rim-lock shim/wire/kit inside the back of the magazine? If so, only short bullet profiles (like hollowpoints) will fit the magazine. Can you post a picture of the magazine?
I have five 7 round magazines and one 10 round magazine that have no issues with Fiocchi or S&B FMJ.