What class(es) of Heart player would be capable of possession? Thief? Page? Heir/Witch?

That’s hard to say, because ‘Possession’ comes in many flavors. A Thief may Possess directly and a Rogue swap bodies, or vice versa. Heir/Witch may be more oriented towards Shapeshifting. If it’s straight up bodily possession, the Thief/Rogue pair seem like the most likely candidates, but I bet you could make a case for every single Class combo.