"Catch up with" is a phrase commonly associated with trying to reach a person or group of people who are ahead of you in some way or trying to get on top of something you are behind on. There are several synonyms you can use to convey the same meaning, including "overtake", "reach", "make up ground", and "narrow the gap". Other alternatives include "get up to speed", "come up to scratch", "be on par with", and "keep abreast of". Whatever phrase you use, it conveys the idea of trying to reach or surpass someone or something that is ahead of you.