You are doing two things here....you are using a contraction....That is = that's AND a possessive. So, it would be that's Elvis's. That is Elvis's _______. That is Elvis's litter pan. That's Elvis's litterpan. That litter pan belongs to Elvis. If you use that last sentace structure...you don't have to worry about what goes where.

When I struggle with a sentance's structure, I change it to something I do know.

I am never quite certain when words ending in 's' get the ' before the 's', or after, with another 's' added... I **think** it has something to do with the way it sounds, and if the word itself is already representing more than one of something.