Well, not sure how it looks in the english version, but in the swedish version you got a couple of entries called "don't roll too often" and "the art of failure" on page 48 (it's part of the intro to the skill chapter).
These combined strongly indicates that the awnser is "no".
When the first mutant fails, something should happen. It shouldn't just be "the door doesn't open". It should create a new (worse) situation for the characters. Could be that the door simply can't be opened (remember, the result on the dice might does not only need to represent the ability of the mutant, they also represent the "outside" circumstances).
I kind of like this approach because it prevents skill dog piling (all players tanding in line to roll and see), but I also dislike it because it takes away some of the spontaneity of the players. Instead of just doing something, it always boils down to who would have the best chance.
So that said, I probably _would_ allow a second mutant to roll for it. At least sometimes (I'd let the exakt circumstances dictate, and I like keeping the players on their toes). And I would let someone help on multiple occasions.
But I would try to add some sort of consequence for rolling multiple times. Such as each atempt taking longer and longer, or each atempt causing noise that draws in monsters. Something like that.