Imagine a tournament/battle royal duel (or even 2v2, 3v3). A great mode to move up the ranks with just yourself or a friend fighting for 1st place! Each rank allowing you to get 1 item of your choice as you move up! You'd never be allowed to sell a previous item, so you have to make the right choice as if certain counter items would be worth.
If people decided to take too long whether due to being a complete tank or not fighting, each player first after so much time has passed would gain a moderate amount of power, then after another set amount of time passed, both opponents would start taking true damage a second (and maybe both gain more power or cooldown/attack speed) as well as reduced healing.
Basic concept of course but I think it could be a fun experience to play with a friend, even with a spectating mode to watch others fight!