Gilgamesh work with Isee set?

I see a lot of showcases of people using Gil with the Isee set, but I just can't understand how would it work with Gilgamesh. Yeah, if he could max it out it would be his best set, but wouldn't he lose stacks at the start of his turn when he self-advances? I cant understand how could he have more than 1 stack at a time, and by that point wouldn't Scholar Lost In Erudition be better?