DWV Piping Dilemma from Adding wall-mounted toilet on one side of back to back setup
I'm getting into a remodel of our small master bath in our 5br/3ba home. The master bath is very small so we have decided that a wall mounted toilet would really benefit the small space with the extra room it frees up. We selected a geberit carrier and duravit toilet but thankfully haven't ordered them yet. I have completed the demolition and discovered I have a couple of problems:
1. There is a 4" CI vent that runs vertically through the wall right where the carrier should go. Connected to this 4" vent are all three bathrooms, so that is 3 toilets, 2 showers, one shower/bathtub, and three sinks. My first thought was no problem, I will just add a sanitary tee or wye that routes the vent stack around the carrier and picks up all of the other vents in the process. This would have been great except for the next problem:
2. The other bathroom on the main floor is right through the wall from the master bath, so that the two existing floor-mounted toilets are back to back and connect into a 4x4x4x4" double sanitary tee below the floor. The top of this tee is the 4" vent stack. So if there was such a fitting as a 4x4x4 "ninetytee" where the two side inlets were offset 90 degrees instead of 180 degrees I could solve this problem again by routing the vent stack off to the side of the carrier, but as far as I know no such fitting exists?
So I have come up with a couple of brainstorm solutions but I don't know if products exist. Your help with these possible solutions or any others you may have would be much appreciated:
Brainstorm solution 1: If such a thing exists (google doesn't seem to think so) I would put a carrier in the wall that serves a toilet on both sides of the wall off the one tank. Downside here is I have to buy another wall mount toilet, and I don't know if one tank can flush two toilets without problems? Does code even allow it? Am I missing any other problems this would create?
Brainstorm solution 2: I could replace the 4x4x4x4 Double Sanitary Tee with a 4x4x4x2 Sanitary Tee With Right Side Inlet and then route the 2" Side Inlet up and around the carrier as the new vent pipe. Questions here is if the 2" vent pipe is big enough for the two toilets on the main floor and the third directly below in the basement? I could run some of the other sink and shower vents through the roof or attic independently if necessary rather than joining them all back into one like they are now. If I use the long radius elbows on the 2" vent pipe does it still serve its function okay? Does code allow this sort of alteration?
Brainstorm solution 3: I spotted this fitting called a Vented Closet Tee - Right - With 2" Top Vent. It looks like if I could bring the floor toilet into the side and the wall toilet in from the top and then route the vent around the wall carrier this might work. Not sure if there is enough space between my joists to do this (about 14")? Why are some of the closet tees baffled and some not? Does code allow?
Any other solutions I haven't thought of???
Thanks in advance!