So, I was making some homebrew stuff when a thought wandered into my head. Since Google has failed to help me find an answer, I'll put my question here.

Assuming it is even possible, what do you think would happen if a caster were to expend multiple spell slots on a single spell simultaneously? Would you be able to cast one of your spells at a stronger level than the slots you wield? If you used all your slots could you theoretically cast a spell that surpasses even 9th level magic without needing the 10th and 11th level spell slots of 2e? Could we even make spells that require multiple spell slots in order for it to be casted, with effects that have yet to be seen? I would genuinely like to see what people think would happen, as I can see some potential campaign material for such an idea.

You make a spell more powerful by casting it with a higher level spell slot.

I can't think of any in-game reason to use multiple spell slots for a single spell.

Edit: OK, one reason - a ritual where each participant contributes a spell slot as part of the ritual.

This is kind of a confusing question because its unclear whether you want to know whether from a game mechanics perspective would or how would this work, or whether you are asking how this would work from a worldbuilding perspective so how the lore of it would work?

If you are the DM you can make it possible so you can pick any of the suggestions you outlined. Personally (and I think is 'as intended') I think of spell slots as a mechanic only, so characters in the world don't use 'slots' they just have a certain amount of magical power to expend each day.

The short answer is no.

The longer answer is absolutely not. The rules of 5e D&D is not in any way whatsoever designed to accommodate such mechanics and attempting to introduce such things would have no established way to balance it. That means you're just asking for either a bunch of ridiculous game breaking results or something entirely underwhelming and generally pointless and probably overly complex either way. You are of course free to attempt to do so using entirely homebrew rules in your own game, but there no official rules for stacking spell slots on top of each other for increased effect. If you want to theorize and discuss such matters, this site has a separate section specifically for that sort of discussion: https://www.dndbeyond.com/forums/dungeons-dragons-discussion/homebrew-house-rules

Quote from Syncraven >>

So, I was making some homebrew stuff when a thought wandered into my head. Since Google has failed to help me find an answer, I'll put my question here.

Assuming it is even possible, what do you think would happen if a caster were to expend multiple spell slots on a single spell simultaneously? Would you be able to cast one of your spells at a stronger level than the slots you wield? If you used all your slots could you theoretically cast a spell that surpasses even 9th level magic without needing the 10th and 11th level spell slots of 2e? Could we even make spells that require multiple spell slots in order for it to be casted, with effects that have yet to be seen? I would genuinely like to see what people think would happen, as I can see some potential campaign material for such an idea.

 RAW, you cannot. One spell, one slot. It's not even something that the game considers to be a possibility. We know this because the inverse case; if you cast a spell with a higher slot that its native level, you don't get change. A L20 full caster (eg Wizard, Sorceror, etc), without using special class abilities, gets to cast 22 spells in a day.  If you cast a L1 spell using L9 slot, you don't get 8 spell slots to use on other things. You just lose the L9 slot - if you're lucky, it'll have a greater effect, but it's almost always better to cast a native level spell than an upcast one. So, messing around with spell slots, either combining them or breaking them apart is not a thing in 5e.

You could homebrew a system. I don't have the knowhow for that. You have to account for the fact that a L2 slot is not the same as two L1 slots. You also want to "tax" it - it has to be more desirable to cast using L9 slot  than to use lower ones combined. It should also be limited by class level - you don't want L5s running around casting Wish. Also account for the oddballs like Warlocks who only have a few slots but regain them on a short rest.

As for L10+ slots, again, there none by RAW, so it can't happen that way. You could homebrew some spells, but I'd be careful. A jump between L8 and L9 can be quite large because you have to wait two levels between obtaining a L8 slot and gaining a L9 slot, plus you can only cast one spell a day of each (or L8 spells). With going to L10 slots, well, at that point L1 slots a like pennies - you're trying to find uses for them. So topping up a L9 slot with a L1 slot is practically free - so your L10 slots really can't be much more powerful (which is why you really want to discourage players from doing top ups routinely, using a L1 to top up a L8 slot to a L9 slot is very powerful).

This is a mechanic that I'd be very wary and very careful in implementing. It could get OP very easily.

I could see a mechanic in which multiple people cast the same spell to extend duration or range. 

You could certainly introduce a mechanism for spending multiple spell slots on a single spell, but it shouldn't do very much (maybe equivalent to metamagic?)

You don't really need a new system, you can just use the spell points option in the DMG. With that system, upcasting and spending extra spell slots are effectively the same thing.

If the answer to that is "but I wanna spend spell slots," I would say that adding a mechanic just for the sake of the mechanic is generally not a great idea. New mechanics only need to exist to describe new concepts that current mechanics can't cover, and "casting a spell really hard" is already covered through upcasting.

I've toyed with a homebrew mechanic that would let you burn an extra spell slot to increase the DC of a spell, but I can't see some kind of stacking upcast mechanic really working in terms of being balanced

Everyone else has pointed out that it's against the rules, but you said you're homebrewing.

Personally, I'd say it's okay if you just treat it like an upcast. Heck Sorcerers Twinspell for technically less and that's effectively using multiple spell slots (because they can turn points into slots). So, if it was a feat (which the  costs a valuable ASI), I'd say that getting to twincast without the sorcery point baggage isn't too big of a deal.

in unearthed arcana 29 there was a wizard subclass called "lore mastery," the subclass had a feature at 6th level called alchemical casting that allowed you to expend either an additional 1st, 2nd, or 3rd level spell slot for additional effects when you use a spell slot to cast a spell. the additional effects are, in ascending order; increase the spell's damage by 2d10, increase the spell's range to 1 mile, or increase the spell's save dc by 2.

this is archived unearthed arcana so take it's balance with a grain of salt, however if you were to include a feature in your games that allows a single spellcaster expend additional spell slots for additional power i'd suggest something like this.