Joist Support Dilemma

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joeymike
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Q:

I have myself a bit of an architectual problem in my 1960s cape cod house. My first floor bathroom, my only one, is pretty small. It had popcorn ceilings when I bought it, so I tore down the whole ceiling to start new and fresh anyway and noticed that the space above was open to the rafters and roof. So I figured id leave it open to the second level, double high ceiling to improve the size of the bath and have great looking vaulted ceiling. Problem is the second floor bedroom extends over into the bathroom space about 4 ft but not quite the center of the open ceiling space. And the wall of it goes up to the apex of the roof. Im fine with having the upper wall there in the center of the bath, thinking of hanging a huge picture frame on it, but the joists that held the ceiling up are in the way, across the whole bath. Id like to get rid of them so its open space but i cant simply cut them because they also support the second story floor. I would cut them to where the upper bedroom wall starts but again; they stick out from the bathroom wall frame 4 ft. and not sure if thats enough to cantilever enough support to hold the partial floor of the second story without additional support from a cross beam or not. My question is what's the best to support this with a beam on the room's adjacent wall frames, or anchor it to inside of the the roof? preferably without puting a support pole in the middle of my bathroom.