The infinity hat and the rest of the set (with the exception of the gloves and boots) can be recoloured by using the hat on an elemental rune altar, after completing the Rune Mechanics quest, with your Rune guardian follower present or in your inventory. It can be coloured to red (fire), blue (water), white (air), or brown (earth). Due to the large amount of pizazz points required, it will take a long time to acquire enough points to redeem a hat.
A dragonbone upgrade kit can be combined with an infinity hat to make a dragonbone mage hat. This is a cosmetic enhancement and does not change the stats in any way.