u/ExternalPen8075

I have an existing deck which measures 22.5 feet x 13.5 feet which is tied into the existing house walls shown in green The joists ride on tripled up 2x10s that are mounted on top of 6x6s. I was looking to add a roof over top of the deck and drew something up using 4x4s, but think I should use 6x6s. My question is can you set a 6x6 on top of a triple 2x10 to carry the roof load?