"Make a date" is a common expression used to refer to arranging to meet someone for a social occasion. However, there are several synonyms for this phrase that can be used to convey the same meaning. "Set a time" is a simple yet effective way to express a plan to meet someone, while "schedule a meeting" can be used in a more professional context. "Arrange a rendezvous" has a more romantic connotation and could be used when planning a surprise date. Lastly, "first make plans" implies that there has been some prior discussion between the two parties and they are now finalizing the details of the meeting.