Honestly, I think with exotics you should be able to upgrade everything apart from their unique effect.
So say, for example, you get the "Tardigrade" Armour System as a drop. It rolls with a core attribute, 2 secondary attributes, a utility slot and the Ablative Nano-Plating talent.
It would be great if you were allowed to re-calibrate the core attribute, both secondary attributes and the utility slot to whatever you wanted from your library. But the talent that gives the armour its flavour is hard-baked into the item and cannot be changed.
That way exotics would be really special, as you can tailor them to your personal taste. And the ability to upgrade multiple attributes on them could be seen as the item being of such high quality, it allows that kind of modification; whereas a set piece or high end piece of gear only allows one, as anymore would compromise its integrity.
It wouldn't be overpowered either, as you would still be limited by the restriction of one exotic armour piece and one exotic weapon. Instead, it would offer an opportunity for those people who have abysmal RNG with item rolls to actually have a couple of maxed out gear pieces, assuming they even wanted to run an exotic (given that some of them are, to put it kindly, lacklustre).