There are several synonyms for the phrase "stands on". One such synonym is "rests on", which can refer to something physically or figuratively supporting or depending on something else. Another synonym is "relies on", which means that something requires or depends on something else to be successful or effective. "Hinges on" is a synonym that signifies something that is pivoting or depending on a certain action or event. "Is based on" and "is founded on" are similar synonyms, both conveying the idea that something is rooted in a particular principle, idea or belief. Ultimately, the choice of synonym should depend on the context and intended meaning of the phrase.