Laundry Room Remodel

Hi. I will be remodeling the laundry room in my basement. Currently a drain comes down from the kitchen above and connects directly to the drain in the basement floor. I do not see a vent branch, so I only assume it's vented in the kitchen wall. Also in the basement is a laundry tub with a P-trap that branches to the same drain used by the kitchen pipe. Between the p-trap and the connection to the basement floor is a vent branch that exists up the basement wall, through the kitchen wall, and eventually to the roof.

Question: can I connect 3 waste lines (kitchen, laundry tub, and new washing machine box with waste) to the same stack? If so, what size piping is required for this stack? Here I'm using "stack" to mean a pipe that connect the vent to the drain in the basement floor.

I do understand that the new washing machine box and the laundry tub will need to use this new stack for both waste and vent, where the kitchen will use the stack for just waste. Correct?

Thanks for any help.