I know the question of venting multiple fans through one vent has been asked many a time, and I have read the posts, but I still have a few questions that hopefully someone can help me with:

I know that using an in-line fan to vent multiple locations while only penetrating the roof once is the simplest way to do it, I don't like the idea of creating a draft in other rooms of the home that do not require the fan to be on. The problem is that I have 4 bathrooms to vent, and I only want to penetrate the roof twice. I am hoping to install two exhaust fans in each of bathrooms in the main level of the home, and duct them separately to the attic, and then join them via a wye/tee fitting right before they join and exit to the roof vent. And then do the same for the two bathrooms on the 2nd floor of the home.

1) Will this work?

2) The fans have the cheapo built-in dampers on them, and I could install an extra damper on the top of each run just before the join together via the wye/tee fitting. I think that because of the long vertical runs, and the fact that the two runs for each vent join together right below the roof vent, that the possibility of backflow of air into the other bathroom is negligible....am I correct?