I see... I wonder then why not use a bushing then?? perhaps this is what OP means by "internal diameter coupler" I think of a bushing or perhaps something in need of a cheater sleeve and I fail to understand how this problem cant be solved with approved fittings....
Okay re-read that OP and I think I get it... so why not just remove the 4" or replace that section with a new 4x3 t wye and some couplers?
Me, I'd remove the section of 4" and bush it down though it may be a pain in the ass if the pipe has been glued in there for a while now... but still doablle,
You will need.
1 hacksaw blade, or dremel, or sawzall ( if your good with one )
1 hammer or rubber mallet
1 Flathead screwdriver
Cut the pipe off at the t wye, then cut down the inside of the pipe only untill you touch the hub. Do this on a few segments if the pipe is glued for a while.
Slam the scredriver in there and separate the pipe from the hub wallwith a twisting motion, You want it to Coil out and leave the hub wall intact. ( vice grips and a twist when you can grab the pipe helps too )
Prime.... wait a fe mins... prime again, Glue.. assemble with a twist and a push..
Done.
Make sure that the center is going to be proper on the bushed down 4x3 with it now going out 3"