Raising heating ductwork

I am finishing my basement. I have a main heating trunk running down the center of the house. It looks like it can be raised up about 4 inches to snug up against the first floor joists. I need all the headroom I can possibly get. . Can this be done? Any idea on cost (I know this is an unfair question). I am guessing I need some sort of transition boot where the duct would get cut. Would this cut air flow if a transition was put in? I don't have much HVAC experience, but it doesn't seem like this would be a huge job. . Thank you for your time.
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Jack wrote:

Maybe have a duct guy come in for a recommendation on where best to cut in any new pieces (furnace, outlest along the main trunk), you could do all the work, and he could provide the specs for extra pieces. What they do around here is sent the specs in to a shop that makes up "specialty" pieces.
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