The end of one of my plumbing runs in the basement (3") is currently a wye. One side has a threaded plug on it for a clean out. The location of my basement bathroom layout has the new drain plumbing right under this so it would be the ideal spot to tie into this existing drain line. The issue is, since this is a wye above, i cannot easily cut this section out to add a new wye to it as I would then have to reconnect the other drain connections from above and space it tight (if that makes sense).
Is it possible to remove existing wye clean out plug, thread on a new wye to the back of the existing wye, put a new clean out plug on the end of the second new wye and add then tie the new fixture drain to this new wye? I thought this would work threaded into the existing clean out and the new wye solvent welded to the back of it. (New clean out plug added to back of 2nd wye)

 

What you've described is common and can certainly be done. I don't see any issue with using the threaded connection to extend your plumbing. As you said, you want to maintain a new cleanout.