What if League had a Custom Item you could make?

What if once per game you could combine random parts into an item? To keep things simple, we'll assume no actives or passives transfer unless they were already in the component items.

To keep things somewhat sane, we'll limit the number of items you can combine to 3.

For example, lets say I want a high AP item with moderate cooldown reduction and some mana regen, but just isn't doing it for me. I could combine + + to get myself an item with 100 AP, 10% CDR, and 50% base mana regen.

Alternatively, if I hadn't used my combinations and it was the late game, I could combine + + to create a 310 AP, 50 Armor item that ignores 35% of enemies armor and gives me a 2.5 second statis.

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So, what would you make? Would you fill a specific nitch that helps your main, or would you save it to create an item of incredible power?