The phrase "buy on" can mean a few different things depending on the context. One definition is to purchase something on credit or with a payment plan. Synonyms for this definition could include "finance," "lease," or "rent-to-own." Another meaning of "buy on" is to make a purchase based on a recommendation or endorsement. Synonyms for this definition might include "trust," "believe in," or "follow the advice of." Finally, "buy on" can mean to purchase something quickly or impulsively. Synonyms for this definition might include "spontaneously buy," "impulse buy," or "buy without much thought".