Hello,
I have 2 daughters and need to upgrade WC situation. I'd like to make sure my DWV design works.

Existing Conditions:
1. There is a 4" cast iron main stack 17" (CL to CL) behind the existing toilet.
2. The toilet connects via wye to the vertical stack with 4" cast Iron trap arm.
3. There is 4" space under joist from the top of 4" trap arm and the cast iron wye.
3. There are 2" auxiliary stack adjacent to where I'd like to install a new toilet. It is used for kitchen drain.
4. The new toilet behind existing kitchen is approximately 12' away from the main stack.

New DWV design and work:
a. Disconnecting 4" cast iron trap arm.
b. Extending 4" pvc from 4" cast iron wye on the vertical stack
c. Installing new 4x4x4 pvc wye with a new 4" pvc flange for exist toilet, connecting to the pvc extension(b).
d. Extending another 4" pvc, 9'-6" to 4x4x2 wye, horizontally connected to new lavatory drain (wet vent).
e. Extending 4" pvc 2'-0" to new 4" pvc flange with a clean out (another 4x4x4 wye) for new toilet.
d. install and connect new 2" dry vent from lavatory to adjacent 2" auxiliary stack above flood line.

I think I can keep the new 12' long 4" pvc section straight without a bent and as much as 1/4" per foot slope to the main stack. The existing kitchen sink shares the same vent with the new lavatory/toilet, but it drains to secondary (separate) drain. I am not altering the kitchen drain.

Is this design work? My main concern is drainage for the two toilets. Thanks !!