There are several synonyms for the phrase "enjoy great demand." One option is "be highly sought after," which suggests that there is a lot of interest and demand for a particular product or service. Another synonym is "be in high demand," which implies that there is a lot of competition for a specific item or service. "Experience a surge in popularity" is also a synonym, which indicates that there has been a sudden increase in demand for something. Ultimately, all of these phrases suggest that something is in demand and highly valued by consumers or clients.