There are plenty of synonyms that can be used in place of "founded on" to convey the same meaning. Some of the most common synonyms include "established on," "built on," "created on," "formed on," "constructed on," and "based on." Each of these synonyms can be used in a variety of contexts to describe something that is built or created on a certain foundation, whether that foundation is an idea, principle, or belief. Choosing the right synonym will depend on the context of the sentence and the specific meaning that the writer wants to convey.