"Closing the door on" is a phrase that suggests shutting something down or putting an end to a certain situation. There are several synonyms available for this phrase, depending on the context of the situation. 'Concluding', 'terminating', 'ending', 'wrapping up', 'finishing', 'bringing to a close', 'culminating', 'ceasing', 'putting a lid on', and 'bringing to an end' are some of the synonyms that can be used in place of "closing the door on". These synonyms can be used in varied situations like ending a business deal, concluding a project, wrapping up a speech, or terminating a relationship. Using appropriate synonyms can make the message clear and concise, and also add depth to the language.