Whipping cream will go bad in MP. (Tried it, got moldy soap) With MP, pretty much anything that will go bad sitting out on your counter, will go bad in MP. Many MP soapers have also had problems with powdered milks getting moldy in their soaps. Which makes sense since MP is a "water based product" and you're basically making milk then.
I'm not a fan of sticking oils & butters in MP because it really doesn't do anything except add label appeal. If after using your soap for a while you still feel like it needs an added butter or oil, I'd try a different MP base, since adding extra oils & butters will decrease any lathering.
As for what you can put in MP: oatmeal, some spices, cocoa, cosmetic clay, calendula, fruit seeds (some do go brown though), salt (don't use dead sea salt because it sweats), you can make sugar scrubs with it, then of course colors & fo's or eo's as well.