The common phrase "close the door on" can be replaced with a variety of synonyms depending on the context in which it's being used. Alternative phrasing includes "shut the door on," "block the door," "bar the entrance," "seal the door," or "put a stop to." Each of these alternatives denotes the action of preventing something from entering or leaving through a door or other access point. Additionally, they imply a sense of finality or resolution, suggesting that whatever is being closed out is unlikely to return. Choosing the appropriate synonym for "close the door on" is based on the specific message the speaker or writer wants to convey.