Concentric venting for a 96%er.

Hello gas gurus. Stepping outside my knowledge with venting for a 96% gas furnace (for one of my investment properties I'm rehabbing and having a relative live in).

My only option is to go thru the roof (existing chimney). There's no option to get it from the middle of the house to an acceptable/approved outside wall.
I have a chimney that has to either be rebuilt (not likely) or I planned to take it down below the the roof line, probably to the ceiling joists. 6" terra cotta lined.

I'm familiar with concentric vents at the roof-run exhaust/intake up to attic separately, then into the roof kit.
What I was wondering was can I (do they make?) a concentric that I can run down the chimney using it as a chase) to the mechanical room (total run <25 feet), then split out my exhaust and intake in the mechanical room? Both pipes wont fit into the chimney separately, and running a separate pipe up next to the chimney requires lots of demo.

Was looking at various furnace manufacturer's install kits. Although they show a concentric under the roof with the kit, I haven't seen one showing it running the entire length and splitting back out at the furnace.

Thanks for your input!
Steve