Some game mode ideas.

I don't think, that any of these should be permanent, but more like into the "rotating system".

Deathmatch: Everyone start at lvl18, homeguard, and 30000 gold. Plates are disabled from start, and dragon spawns at 2. min., Baron spawns at 5. min.. Only elder dragon spawns.

Gangster minions: Minions come with guns, and stronger than ever. Even worse, that they focus champions if any champion gets into range. Minion last hit always considered as executed, and if minions kills you, then you lose gold. Simply farming would become one hell of a task.

Super jungle: Each jungle minion is massively buffed, and all of them gives team wide gold for killing. Which means, that jungler as role is erased, and going into the jungle to clean is a team effort.

Vengeful turrets: Whenever a champion in turret's range gets damaged by an enemy champion the turret gains +500% attack, and vision range, +2.0 attack speed, and prioritize enemy champion with the lowest health for 15 seconds.

Shared burden: Any gold, and experience income from any source shared for the entire team. (You kill an enemy for 300 gold, then you and your teammates get 60 gold each instead.)

Harsh death: Same start as Deathmatch, but respawn is disabled. Your team only respawns, if you lose, or destoy objective. Minions, and jungle no longer grants any gold. Killing Baron, or Dragon is considered objective.