wet vent toilet

Hello all and thanks for any assistance you may provide. I wanted to add a small wet bar sink to my basement. I planned / installed an AAV for venting. The problem is the drain would have to cross the vent stack from the existing toilet. Initially, I was going to keep that vent horizontal...

I am remodeling one unit in a duplex. The tenants before have had issues with the toilet backing up into the shower. I want to add a vanity (only) behind the shower into the master bedroom but I don't want to make the issue worse. I have taken several pictures and spent many hours under house...