A synonym for ‘based on’ is ‘derived from’. This phrase is often used to indicate that something has its origin or foundation in another thing. For example, you might say, ‘The movie was derived from a true story,’ meaning that the movie’s plot was inspired by real events.
Other synonyms for ‘based on’ include ‘founded on’, ‘grounded in’, ‘rooted in’, and ‘built upon’. Each of these phrases can be used depending on the context to convey a similar meaning.