As you know radiance is one of the hardest item to buy in the game and hand of midas is one of the most useless item in the game. So I have an idea, why not combine them?
Basically, 550 gold for tranmute and 30% attack speed to be added on radiance.
Now it's much easier to get a radiance and midas is no longer useless!!
It also fit the theme - midas hand + sword = golden sword!
Many people has been arguing this item will become a must for farming hero, but it should be balanced by the fact that this item is mostly one per team since the burn damage don't stack.
Edit (4/3 wow its been so long): Sorry have to make sure it works. If this method doesn't work please tell me (I'm only 95% sure). Radiance can be turned on and off by checking the slot it's in. For example, I'll let radiance turn on if it's in slot 1 and off if it's in other slots.
I think the number problem can be solved by adjusting sacred relic since the only other item using relic is rapier. Ice Frog can reduce its damage to 40 and its price at the same time and then add a recipe for rapier.
Edit 2: slot 1 to 1,3,5
Edit 5/31: removed transmute to encourage more fighting and less nerf to chen.