I am looking to install a new bathroom in my basement. The first attached diagram shows my current setup with a 1st floor bathroom running to a sewer connection through pipe that runs under the basement floor. A prior owner of the house had a toilet installed in the basement sitting directly on the waste pipe under the basement floor to the sewer. There was no other rough in for shower or sink. The 2nd diagram shows my proposal for completing a full bath group install in the basement. The toilet would be moved about 2 feet and be connected to the existing toilet drain with pvc via a back outlet unit. The basement floor would be "dug up" and a shower drain installed about 2 feet away connecting to the same existing drain (previously used for toilet). A sink would be installed and also drain via pipe in a wall to the same existing drain (previously used for toilet). So, do you think I can use the existing toilet drain and connect the toilet, shower, and sink all at this one location? I visualize cutting out the existing connector to the existing toilet and replacing with some kind of connector that has a horizontal connection on earch side (one for new toilet location, one for shower) and a connector on top to terminate the sink drain. Also, the 2nd diagram shows air admittance valves at 2 locations for venting. I am not able to accommodate vent connections to existing vent system. Do I need AAV's at both the sink location and the shower location. The shower location would be accommodated by placing AAV in a wall that will be built. Would this venting meet code? Thanks for your help.