There are several synonyms for the phrase "for the greatest part", which means mostly or primarily. One of the alternatives is "largely", which signifies mainly or chiefly. Another option is "mostly", which is used to describe something that is predominantly true or applicable. "Mainly" is also a synonym, implying that something is primarily true or exists to a great extent. "Predominantly" is a more formal alternative that suggests something is the most important or prevalent part. Lastly, "chiefly" is a synonym that denotes something as the most important or significant part, with other parts being secondary or less important.