New Sewer Connection

I need to tie into my existing 4" PVC sewer pipe, which runs under the dirt floor in my basement, for a new bathroom. The new line will enter at 90 degrees and also needs to be beneath the dirt floor. I plan to pour a slab in the future. I plan to expose and remove a short section of the existing pipe, glue a 45 Wye onto the downslope pipe, use a fernco to attach the upslope end, and then glue the new line to the wye with a 45 degree elbow. Doe this make sense?

Anyone have any suggestions on this one? I would appreciate your help.

Sounds like a plan, I'm just wondering what the rest of it is.

The new full bathroom is on the opposite side of the house from existing 4" line on 2nd floor. The new 3" toilet drain will run from 2nd floor to basement ceiling, then 90 degree bend (w/cleanout) for about 15' along basement ceiling, then 3" tie in from new first floor powder room, then 90 degree elbow and drop to floor along center stone foundation wall, then 90 degree elbow under dirt floor and stone foundation wall to existing 4".

Hmmm I didn't hear cleanout in any of that description. Can you post a sketch?