Will this bed liner adhere to a spray on liner already in the bed?

We would need to know what the prior Bedliner was made of. If a plastic drop in, we recommend remove it and spray onto the truck bed itself since applying any coating to plastic is problematic. If your current bedliner is peeling, top coating a failing Bedliner will be disastrous. If the current bedliner is intact, it would have to be heavily abraded/ sanded to give it any chance of success. Try applying some on a small obscure area of your truckbed.