There are many synonyms for the phrase "at a profit", including "with a gain", "profitably", "successfully", "remuneratively", and "advantageously". These words all suggest that the entity or individual in question has made a financial gain, either through a business transaction, investment, or some other means. Other possible synonyms include "lucratively", "beneficially", "productively", and "fruitfully". Each word carries a slightly different connotation and may be more suitable depending on the context in which it is used. Regardless of the specific word chosen, all of these synonyms convey that the person or company has made a financial profit from their actions.