Ok, let me outline a couple of scenarios.
1) Thor couldn't possibly wield his hammer and Cap's shield as weapons in the same action, so if Thor picked up the shield, he'd have to make a choice. That much is fine.
2) Let's say there's an alternate universe where Spider-Man happens upon the Crimson Gem of Cyttorak (which, by the way, you can find a writeup for here: http://wp.me/p2gNim-70
, written by yours truly). He still has his Spider-Man powers, but now he is also the Avatar of Cyttorak with the powers of the Juggernaut. He'd have three Power Sets essentially. the implications of what things would look like in that universe are staggering, but you see where I'm going. There's not any huge reason to restrict Spider-Man because of this. The Watcher could whip something up (Cyttorak's powers are mutually exclusive from the Spider abilities because Cyttorak is afraid of spiders, Peter Parker's wrists are too big to wear web-shooters, etc.), but it might feel a little wonky, especially if a player has the image of an oversized Spider-Man charging up the side of a building like a freight train.