It's feasible but this is entirely up to the power company. I had a project one time for an existing building where the existing service conductors between the Utility XFRMR and meter center were damaged by a saw blade, so we had to put in a hand hole to pull out the damaged conductors and we had to get special permission in writing from the power company to tap the existing service conductors.
Personally, I think the bigger issue could actually be voltage drop. Fire Pump feeders are required have a voltage drop of less than 15% under Locked Rotor Amp (LRA) Conditions. Assuming 208/3, the LRA of the 75HP fire pump would be about 1200 Amps, and then you have to add the demand amps of the non-fire pump loads to that.
What is the calculated demand of the "normal" loads on this service, and how far are you running?
FYI: If this is new construction then its probably a new transformer. The power co should be a able to put an additional cabinet next to the transformer to land additional conductors. The easiest thing may be to just email the power company.