Yes, you can definitely do both!
Really, unless you are in the camp of wanting to do the strict simeons diet only, which if you are that’s totally fine and we respect that, the AP version is actually meant to be done on top of/in addition to SP.
Basically meaning AP allows all the ingredients that SP does PLUS the AP ingredients. It’s basically just an expanded protocol of allowable ingredients. So if you are following AP, you would not need to eliminate any foods on the SP list (unless you are finding you stall with any of them).
But take note that sometimes an AP ingredient might make someone stall- it’s not for everyone. Certain AP ingredients might be fine for you, and some may not. It’s all an experiment. But many ladies do use them with success.