Please Assist!! Adding second vent/soil stack
i am adding a second 3" vent/soil stack in the south end of the house. main vent/soil stack is in the middle of the house about 25ft downstream. previous owners installed WC, bathtub, vanity in basement with no venting. since i am redoing 2nd floor room, main floor kitchen, and basement bath, i thought to add this second line to vent and drain all the new and old stuff. please see the attached sketch. I think I am ok, except where the WC is involved. Do i need to add a vent line off this back to this new vent stack? Any help is appreciated.