The possessive, masculine, plural form would be "suoi", and would be preceded with the plural, masculine definite article "i". "sui" is the contraction of "sul" (on) and "i" the plural definite article for divano. For "the cats are on their couches", I believe you would have something like "i gatti sono sui suoi divani"
EDIT. Pay attention please!
What is written above is not correct.
"Sui" is not a plural article. "Sui" is what in Italian is called "preposizione articolata", meaning the unification of a preposition plus an article.
SU (preposition) + I (plural article) = SUI ("preposizione articolata").
You don't have this in English.
"The cats are on their couches" is "i gatti sono sui loro divani" - "I suoi divani" is "his/her couches".
I have to disagree. Cats own everything in the house, including the people who clean their litter boxes, feed them, and take them to the vet. Sometimes, just to see if you are paying attention, they try to trip you on the staircase. Their job is to sleep all day on the divan. It seems fair. To them.