The only wayto to accuratly determine demand is do the hydraulic calculations but I am pretty sure it would work just fine for sprinklers.
Figuring an average of 90 sq ft. per sprinkler we would have around 16 sprinklers to calculate each discharing 15 gpm.
240 gpm for sprinklers but this would approximate a theoretical minimum so to be on the safe side I would add 25% for 300 gpm.
Friction loss through just the pipe on the top floor might be 40 psi but, seeing how it is pipe schedule, I doubt it's that high but let's use 40 anyway.
7 psi end head pressure.
40 psi friction loss through overhead pipe.
If fed by old 6" standpipe the friction loss would be negligible.
12 stories so let's figure 12' between floors for a max height of 144 feet. Elevation loss would be 63 psi.
Total loss, ore pressure demand, would be 110 psi or less.
95 psi pump and say 50 psi from city we have 145 psi available. I would have to think you would have at least 145 psi @ 500 psi available at pump discharge.
100 gpm added for hose stream and I don't see how total demand would exceed 400 gpm at @ 130 psi.
I don't for the life of me see how this wouldn't work unless something is really wrong but, as I said, we need piping layout and distances to be sure.