The phrase "keeps up with" means to remain at the same level or pace as someone or something else. There are many synonyms that can be used in place of this phrase. For instance, "keep abreast of" indicates that one is staying informed and up-to-date on the progress of a task or project. Other alternatives include "keep pace with," which suggests that one is maintaining the same speed or rhythm as others, or "keep in step with," which conveys a sense of coordination and synchronization. "Keep pace with" can also be used, which implies that one is keeping up with the latest trends and developments in a particular field or industry.