What if you could enchant legendary items for 1000 gold to give them unique passives/boosts?
I mean, I'm sure we can all think of something that could make items better. Would it be broken? Not if both sides are allowed to use them. That, and people would have to choose between starting their next item and enchanting their current item. It would allow more customisation, enhance specific play-styles, and most importantly, make the late-game more important.
I'm sure Riot can use their magnificent brains to think up something nice, but here could be some really simple suggestions. You can only pick one of the three, as well.

- Grievous wounds applies to champs below 70% health.
- Deal 1% bonus magic damage to champs for every 2.5% below 40% health, up to a max of 16% damage.
- Dealing damage to champions below 40% health increase the range of your targeted abilities against that champion for a short duration.

- Warmong's Heart heals faster.
- Passive completely ignores damage from minions and non-epic monsters.
- When Warmong's Heart is active, take 30% less damage for 3 seconds after taking damage.

- Critical strikes lower your remaining cooldowns by 7%.
- Critical strikes deal 50% of the mana you spent during the time between your last crit as bonus physical damage.
- Critical strikes return more mana.

- Damage increases against each champ with every tick of damage they receive in a row.
- Damage slows champs after the third tick.
- Radius of damage increases with bonus armour.
Come on, anyone can think of small ideas like this. Give it a try!