I'm curious, what spell combinations do people think would break the game if you could concentrate on two spells at once? Feel free to use any spell class list, including multiclassing, to answer the question.
I've thought about making this an archetype feature, specifically for a "Mage" wizard archetype who was supposed to be an answer to the AD&D 2e generalist, and a "Songweaver" bard. The feature didn't make it into either final version due to balance concerns, but I ask the question above because I never really took the time to explore how possibly broken it could be.
In any case, the "Mage" version of expanded concentration was their level 14 archetype feature. It was a simple feature, lets you concentrate on two spells at once. No real penalty or constraint for doing so, but if you had to make a concentration check, it could fizzle both effects. Worth noting that some balancing was done against his other archetype features, which were even more ribbon-y than other wizard schools. If I felt like revisiting the idea, I'd probably put a limit on the spell slot you can use on one or both spells, maybe 3rd of 5th level. The Songweaver was a bit different. You could spend a point of bardic inspiration to extend an effect for an additional round after concentration ended. It was a quick way to run out BI, but my experience with bards have been that they don't use BI enough anyway, so I was kind of happy with it.
Neither archetype ever saw live play, so the ideas remain essentially theorycraft.
Back to the OP, I don't think this should be a general spellcasting rule. Magic users have a big enough advantage over martial classes already, no need to widen the gulf. I like it as a possible archetype feature for a homebrew, as I did in the aforementioned examples, but tacking it on as a freebie class feature feels way too generous to me, even if it does have significant constraints. There should be a cost to selecting this option. Thus, it could also be functional as a feat, though I would want to see some constraints here, too. Limiting it with a spell slot level cap would be a good step in the right direction. I heard disadvantage on concentration checks earlier, that would be reasonable to me, too.