How to create inventory slot that stores more than 64 items

I would like to create a slot in a tile entity inventory that can store more than 64 items. I am aware that there is a max stack size option, but that doesn't change anything because other items have their own stack limits. What im asking is if there is a way to bypass the item stack limit and allow more of the item to go into the slot, if that is even possible.

Thanks!