Now i get confused: All comments and references in this thread so far lead in 2 opposite directions. I boil it down to this question: What is the superior "ability" of possession? Continuing player A's control or giving player B an extra turn? Is it more like Tribut (A benefits from B's cards) or more like Golem?
On an abstract level: Is the flow of game by players or by turns? I think by former, because we switch from one player to next after whatever number of turns a player have. Ok this could be also an argument for the latter but I empasize the control of hands, not whose hands it is.
If by players, then any pending Possessions of one player should be resolved, before the next player can play her/his turns (regular and further extra in whatever order). Similar to "+ 1 buy" a Possession could be seen as "+ 1 turn" (although played trough next player), so any Possession during possessed or "own" turns would cumulate and resolved after each players turns with her/his deck and before giving control to next player.
That would make
A possesses B two more times and then B plays his normal turn and then B possesses C three times and then C plays his normal turn, provided there are no more plays of Possession.
the correct answer to OP's question. For
Player A plays two Possessions in his turn. During the first possessed turn of player B, he plays Outpost.
Possession 2 - regular B
and no extra from Outpost would be the right order.
If by turns, then player B can decide wether the second Possession turn or the Outpost turn goes first. Furthermore a chain of
Possession played in a possessed turn leads to resolving these first. After how many of these (perhaps spiced up with some Outposts?) does one loose track
(pun intended) whose regular or extra turn is next? With
Possession says "The player to your left takes an extra turn after this one." (Emphasis mine). That means as soon as the currenet turn ends. It will not wait for player B's regular turn to end.
OP's question could be resolved to
B possess C 3 times - A possess B 2 times - B's regular - C's regular provided there are no more plays of Possession. But other solutions are also possible. Who may decide? Whose Possession(s) is "primus inter pares"?
So long Donald does not say otherwise I go possessed turns first then unpossessed turns! And if there are more Possessions, they get resolved if the players other turns are done.