I think this kind of an idea would be a good PVE game. Just endless waves of minions, yours stay the same strength always, but the enemies constantly get stronger. Every 3 waves is a super wave, which starts off with just the standard cannon minion, and then upgrades from there. And After every 12 waves, the default wave upgrades, getting stronger and stronger with every 3 waves after that. Possibly could get to a point where the waves are full super minion waves, and after you survive 100 waves, it sends a boss wave, and if you survive, Victory. I'd put this in Summoner's Rift, and have the waves start off in every lane, then as you approach "mid game" they shift lanes, but your minions still spawn, so you may get a random tower just from minions pushing in.
Victory would be achieved through either killing the boss wave, or destroying the enemy nexus (which would have increased health, along with all towers and inhibitors), while defeat is either A. 10 Aces, B. Destroyed Nexus, or C. Being Aced by the Boss wave.
I'd design it so that if either your team gets Aced, or a tower on your side gets destroyed, all ally and enemy minions are destroyed, a replica of that wave is spawned, and the wave number doesn't increase. And you can make it a little PVP, like Dominion where you see point values for things you've accomplished. Make each of the jungle camps have a unique buff designed to assist in wave clearing (like wolves spawns a wolf companion who attacks enemy minions for the duration, raptors makes your attacks penetrate armor/mr, ect.) Make Dragon and Baron slightly easier, and instead of Dragon Buff and Baron buff, they have bonuses for the ally minions. So first dragon causes you to always spawn a cannon minion, 2nd replaces a melee with a super and a ranged with a cannon, 3rd replaces 2 melee and 2 ranged, 4 replaces all of them with no extra cannon minion, and the 5th timed one spawns the next 3 minion waves with the Banner of Command buff (which will be necessary as some of the further waves will deal magic damage.) While Baron buff can cause next 9 minion waves to have Baron buff. Inhibitor being down will spawn minions with increased stats.
I think for the boss wave, make it a champion down each lane that has full ability usage, but a champion who has a stacking ability. So I'd have 
in top lane, 
in mid lane, and 
in bot lane. having 700 ish stacks, with about 800 AP, and with an extra 2000 Health. they'd hurt, even for a tanky team.
Just my idea.
, because its passive can get pretty powerful. Then there could be custom summoner spells too. Like one could be to convert one minion to a super minion, would be a huge cooldown. And another could turn a minion into health or/and mana depending on how much health is left. And who knows, a new minion could be added as well!
would do well in this mode