Can I apply your floor coating over a painted surface?
There would normally be no problem anticipated if the existing paint is in good condition, but you would be well advised to first test a small area to ensure solvents do not cause it to peel. When mixing our liquids with the powdered component, it is sometimes necessary to add lacquer thinner (standard type, not the “green” type) to thin to a consistency suitable for the application method. This lacquer thinner will evaporate quickly, but could soften the paint before doing so depending on the paint type.
Applying a bit of lacquer thinner to a small area, allowing it to dry, then testing to see if it is still as durable as the surrounding area will help you determine any effect. Also, try scraping the existing coating a bit to determine how well it is adhering. Remember that ANY product which is applied will only stick as well as the surface it is applied to.