There are various similar phrases that can be used instead of "keeps an eye on". Some of these include "watches over", "monitors", "keeps a close watch", "surveils", "observes", and "tracks". Other phrases may include "stays vigilant", "maintains constant oversight", or "remains attentive". These phrases emphasize the idea of being watchful and attentive to something or someone. The use of synonyms for "keeps an eye on" can be useful to vary one's language, add nuance, and avoid repetition in writing or speech. They can also provide a more descriptive and expressive way of communicating active carefulness and attention.