I am planning a screened in deck where my ridge beam is centered on a sided, pre-fab chimney chase that is cantilevered out from the house. The best I can come up with on how to support the beam involves rerouting the flue within so the beam can access the 2nd floor rim, or some method of forking the end of the beam around the flue. A sliding glass door to the basement is below the chimney it so additional piers, posts or beams get in the way quickly.
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Of course, you are not ledgering the deck to the cantilevered chase.
You can set a perpendicular beam below the ridge beam inside/outside the face of the chase.
Use the sidewalls of the chase (extended if necessary) to carry that portion of the roof.
Bring new posts down from the beam to the deck, flanking the chase.
Bolster up the joists under these posts and sidewalls of the chase to carry the load back to the deck ledger at the house. (Structural Engineer or knowledgeable architect needed for right-sizing joists)
Bolster up the joist/ledger AND the ledger/wall connections here.
Try to make sure they don't land above the sliding door so you don't have to increase its header. With planning, you might be able to use the slider's trimmers as your 'posts' to the foundation.
After some pondering, I think I can run my deck joists into the cantilever so that they rest on the sill plate. Then follow ktkcad's advice and run a post or two up the chimney chase to support the ridge beam. Running them on the outside would be easier, but running them inside the chase will look better in the end. I just need to finish my drawings and then we'll see what the permit people think of my plan.
You’ll need to spec the headers and ridge beam size and makeup for inspection. A good lumberyard will be able to submit your drawing with spans etc shown to their lvl supplier who will figure what you need to hold this thing up.
Best of luck!