What are the parameters for Kanai's Cube when upgrading rare items?

Solution 1:

I can now attest first hand that set items are possible, got a Uliana's Strength upgrading a rare shoulder piece with my monk.

With these 2 reddit's threads confirming this also, I'm confident enough to say that the items upgraded will all be for the class they are being upgraded with. Else, set items would not be 100% sure of being for the class upgrading the items which would seem strange.

That is also consistent with crafted items that have stats for the class crafting them.

But, the class-only items will roll with their class stats. I tested with a voodoo mask and got