I think requirements vary from city to city. I've gone thru this several times on retail sites.
Check with your city's building zoning or building permit section. If they are not the right dept. they can point you to it.
I know that you can get variances. Hypothetical: A grocery store and a fitness center are both likely zoned retail or commercial. A grocery store is going to need more spaces than a fitness center. The ordinance is based more for the grocery store so you may be able to get a variance. It will take awhile, probably, but your architect should have some average parking space numbers for fitness centers or a fitness center operators magazine (call them and inquire.
You might be able to borrow or lease a few spaces from a neighboring site if it is already developed.
Hope you have a little time figured in - it likely goes through the plan comission then city council for approval as they have to give neighbors a chance to oppose.