An FM antenna on an AM tower is not that big a deal. Two primary considerations: 1) wind loading capability of the tower, and 2) if it's a multi-tower directional array.
At a minimum, the condition of the tower should be determined by a tower contractor to ensure that it will not be compromised by adding a FM antenna and line.
If it's a series fed tower (insulated base) an isocoupler will be needed in the FM line. If it has a grounded base and is shunt or skirt fed, no isolation is needed. In either case, after the installation is completed, a base impedance measurement of the AM station feed point would need to be conducted and a FCC filing requesting direct measurement of power for the AM be completed (it would probably be a condition of the FM license anyhow).
If the AM is a directional, as mentioned in another post, a partial proof of performance would need to be conducted and filed with the FCC (again probably a condition on the FM license). The caveat here is, it is possible that the AM array is not within licensed parameters already, and a partial proof would serve to prove it. To restore the AM array to licensed values and pattern could be very costly - 10s of thousands. That's a can of worms not worth opening unless this tower is absolutely the only one available, and land use regulations prohibit a new tower.