If Slaanesh takes control of an opponent's cultist, we already know that he gets the benefit of that cultist's upgrade, too. This particular one allows further summoning, though. My question is what happens in Slaanesh takes this cultist and summons it to a place that would normally get this benefit, what happens? Does Slaanesh get a second Clan Rat, and if he does, what's a legal source for summoning? Can he summon from the board as well and/or stockpile? I already know that if Slaanesh controls 2 Clan Rats, he could move both of them just fine. Summon = move, after all, and he clearly controls the second Clan Rat.

No real issue. The clan rat upgrade doesn't affect Slaanesh in any way, since Slaanesh has no rats in stock to summon - in the same way that none of the gods can summon more units than they have stock of.

It's similar to cards that tell you to place old world tokens. If there are no more in stock, none are placed.