I'm going to start with this bit, because it is probably the one that will run away from you the most:
or to allow them to affect multiple targets with a spell that only affects one. This could could work in place of/combined with Inspiration, to roll advantage, etc.
In short, the targeting restrictions on spells, and concentration usually exist for a reason.
If we take an example low level spell, hold personhold person, then we find that being able to disable two humanoids is going to be extremely powerful. Since the spell isrequires concentration, disabling two people would normally require two casters concentrating on two different spells, and 2 spell slots used.
regardingRegarding this:
Combining attacks allow one PC to deal double damage, at the expense of their own:
The Fighter wants to combine attacks with the Barbarian, to double the Barbarian's >damage (2d10 total), at the cost of the Fighter's damage (d6).
- The Fighter wants to combine attacks with the Barbarian, to double the Barbarian's damage (2d10 total), at the cost of the Fighter's damage (d6).
whatWhat is to stop the wizard doing the same? tradingTrading in their d4 dagger hit for double the barbarian damage? thisThis scales well at early in the levels, but at later levels, when the barbarian hits for 2d12 or 3d12, doubling that becomes a lot of damage.
Reroll (damage/)to hit
This is the ouvreoeuvre of the divination wizard, and theywho get two of these result alteringsalterations per day, in exchange for specializing in a school that mostly has non-offensive spells, and spells that focus on knowledge and understanding.
So before you implement this change, consider ifwhether you are stepping on the toes of feats or class abilities. (luckLucky springs to mind.)
And in regards to using inspiration i, I think quoting Adam Koebel on inspiration is relevant here:
if iI go into an important roll without inspiration i effed, I [screwed] up
Your idea seems cool, i'mcool; I'm just trying to point to where it might not gel well with current systems.