When it comes to synonyms for the phrase "closes door on," one alternative is "shuts out." This phrase can be used to describe the act of excluding or rejecting someone or something. Another phrase that can be used as a synonym is "puts an end to." This phrase describes the act of bringing something to a stop or terminating it. Additionally, "blocks out" can be used to describe the act of preventing something from entering or interfering with a situation or process. Lastly, "closes off" can be used to describe the act of blocking access to something or preventing communication between parties.