The phrase "already purchased" implies that a particular item or service has already been acquired or obtained. If you're searching for a different way of expressing this idea, there are several synonyms that may be suitable. "Bought," "procured," "secured," and "obtained" are all words that can be used to indicate that something has been obtained in the past. Other synonyms for "already purchased" include "acquired," "possessed," and "owned." Regardless of which term you choose to use, the important thing is to convey the idea that something has already been obtained or acquired, either in writing or speaking.