The answer
IRC Section R908.3.1.1 prohibits overlays if the roof already has two or more layers, or if decking is rotted or water-soaked. NRCA and ARMA strongly recommend a full tear-off to inspect the wood decking, install self-adhering ice-and-water barriers, avoid heat entrapment, and prevent voiding manufacturer product warranties.
Sources
This answer is drawn from the standards and guidance below. It is general information about how these systems work — not a diagnosis of your property.