The phrase "not allow" has several synonyms that can be used interchangeably in various contexts. One common alternative is "prohibit," meaning to forbid or ban. Another option is "disallow," which is a more formal way to express the idea of not allowing something. "Forbid," "restrict," and "ban" can also be used as synonyms for "not allow," each with its own subtle differences in meaning. Similarly, "denied," "refuse," and "decline" can be used in situations where permission has been requested but not granted. Ultimately, the choice of synonym will depend on the specific context and tone desired, but all options convey the idea of something being prevented or disallowed.