Soil Stack Offset?

[DIYingInMyHouse]

I'm building a 1 and 1/2 story home under 2006 IRC, and trying to lay out the upstairs soil and vent connections. The 3" connection from upstairs WC to the main horizontal building looks like an opportunity to vent the system. In my drawing, the upstairs WC drains horizontally about 5 1/2' before dropping through a 1st floor wall to the soil drain in the crawlspace.

1. Can I wye (or tee) a vertical vent between the WC and the wall? That would provide heighth to join in venting for upstairs fixtures, plus a convenient spot to pick up venting from the first floor.
2. If I use a wye with its inlet turned vertical in that upstairs drain/vent connection, may I also tee in the lav waste drain? Alternatively, I could squeeze a wye combo horizontally into the WC drain, but that means drilling through a floor joist.
3. What do you call this line? Would it be an offset in the soil stack?

 

[DIYingInMyHouse]

Argh! My house really isn't on its side! Sorry about the rotated drawing. It should be 90 degrees CCW.

 

[Sponsor]

 

[DIYingInMyHouse]

I'm building a 1 and 1/2 story home under 2006 IRC, and trying to lay out the upstairs soil and vent connections. The 3" connection from upstairs WC to the main horizontal building looks like an opportunity to vent the system. In my drawing, the upstairs WC drains horizontally about 5 1/2' before dropping through a 1st floor wall to the soil drain in the crawlspace.

1. Can I wye (or tee) a vertical vent between the WC and the wall? That would provide heighth to join in venting for upstairs fixtures, plus a convenient spot to pick up venting from the first floor.
2. If I use a wye with its inlet turned vertical in that upstairs drain/vent connection, may I also tee in the lav waste drain? Alternatively, I could squeeze a wye combo horizontally into the WC drain, but that means drilling through a floor joist.
3. What do you call this line? Would it be an offset in the soil stack?

So maybe a photo is worth a couple more words...I mocked up some of the piping: one photo is from below, showing the WC drain into its 3" line heading through a wye and then to a wall. From upstairs the 2" pipe picks up a drain from the lab on the right, then becomes venting with an inverted cross tee gathering vents from elsewhere before exiting through the roof. The level indicates a knee wall that will be framed behind the toilet. Will this meet IRC 2006 code?