Just a thought. I haven't taken to time to consider the ramifications, so it might be dumb. But how about: set a DC. (Say it's DC 10 in a d20 system). The players that roll above the DC pool together their points above the DC. For example Alice rolls 18, Bob rolls 13. They both beat DC 10, so they start with 10 (basic success in the collaborative task). To that, we add 8+3, for a total roll of 21. Thanks to their collaboration, they beat the DC by 11.
That way, they still both have to roll and beat the DC (the idea is that you have to be competent to offer a contribution of value), but the final result (21) is truly a collaborative score, it's not any one PC's roll.

Now that approach has issues.
1) GMs need to define clearly what counts as a collaborative action and what doesn't. If not, it becomes easy to trivialize anything if the whole party rolls for it.
2) The system must support scaling success. If beating DC10 is enough to succeed in exactly the same way as DC21, there's no point whatsoever to the cumulative points. So, scaling success. Or alternatively, maybe points get cumulative past-half DC, and that half-DC represents the minimum competence floor? (Like, the actual DC is 20, but you add points you got past 10, so Alice and Bob barely made it).
3) DCs need to be calibrated ad-hoc and adjustable according to how many players participate, because a DC for a collaborative task is gonna be impossible to make if a player tries it alone, and inversely the DC for a single-player task is gonna be trivial if they get help. Which goes to reinforce 1) : it's easier to decide in advance which tasks allow for cooperation (maybe even require it), and which don't.

To note: if Cathy decides to help Alice and Bob and rolls a 6, there are two ways to handle it: either she didn't beat DC10 so she simply doesn't give a bonus, or she actively gives a -4 malus (in this case, making them fail). Doing the latter could help mitigate 1) and 3), but it also could maybe make a bad roll too punishing for everyone. I still lean towards it.

So with that idea, I feel like it could work, but requires case-by-case GM adjudication to make sense. There are tasks where you can collaborate and tasks where you can't. (Decide the nature of the roll). Then there are tasks where everyone can lend a hand, like pushing a boulder or solving a riddle, and tasks where only a limited number of people can, like playing a doubles tennis game. (Decide the number of participants). Finally, there are tasks where only a certain limited amount of competence is needed, and an incompetent person is merely useless, like assembling furniture - and tasks where one single incompetent person can really screw it up for everyone, like a baton passing relay race. (Decide if failures are neutral or detrimental). Actually, for that last one, you could make the case that truly collaborative actions by nature (instead of merely "help another") are ones where a single person's failure IS detrimental, and thus always apply the malus.

What do you think? Too complicated, too much micromanagement?