There are several synonyms for the phrase "look for". One common synonym is "search", which is often used to describe actively seeking something out. Another synonym is "hunt", conveying a sense of intensity and focus in the search. "Seek" is another synonym that emphasizes the thoroughness of the search, whether for physical objects or intangible concepts. "Scour" is a more dramatic synonym that suggests a more exhaustive and desperate search. "Explore" is another option, highlighting the sense of curiosity and discovery involved in the search. Finally, "pursue" can convey a sense of determination and persistence in one's efforts to find something.