What I intend to do is just replicate what is already there and (presumably) passed code when the house was built. Right now, I have two bathroom exhaust fans (in separate bathrooms) each venting through what I consider to be unreasonably long runs of 3" vinyl flex hose (each fan has its own run of hose). The two 3" runs of hose both terminate at the same point at a single 4" roof exhaust (a hole cut in my roof with a metal cover about 3" above the shingles). Each flex hose just empties into the roof exhaust.
What I intend to do is re-route each exhaust fan run using either rigid metal duct or flexible metal duct. The two 3" runs will join at a wye which will be connected directly to the single 4" roof exhaust.....essentially the same thing that is happening now but without the wye. I really don't think I will get much, if any, backflow from one exhaust fan to another since the exhausted air from one fan, like all things in nature, will take the path of least resistance and exit through the 4" tunnel to through roof 5" away and in the direction of the airflow rather than reverse its course 180 degrees to push back against a 3" "tunnel" of air to flow back through the other exhaust fan (which is probably 15 feet "upstream").
I am still looking for a 3"x3"x4" wye or a 4"x4"x4" wye. I checked HD in Wake Forest and on Capital Blvd with no luck (they had both 6" and 8" wyes but no 4").