I have a large feed of ductwork from my AHU to a couple of vents in my living area and then a branch of diameter ~13.5" going to the master br/ba/closet (4 vents). My daughter's room is the last in a series of 5 vents and is only fed by a branch of ~9" diameter. Her room is often hot and our room is often too cold if we try to keep the front 2 rooms cool. I would like to break off a branch from the feed to the master br and bring it directly to my daughter's room. I think a 10" diameter feed would work. Can I do this at the first breakout point (vent) or is there another method?

TIA