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Synonyms for Overlay (same or very similar meaning)

WordNet sense 1 (protective covering consisting, for example, of a layer of boards applied to the studs and joists of a building to strengthen it and serve as a foundation for a weatherproof exterior):
sheathing, overlayer

WordNet sense 2 (put something on top of something else):
cover

WordNet sense 3 (kill by lying on):
overlie


From the ODE community, based on WordNetadd/edit