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Wiktionary
open relationship

n. A romantic and/or sexual relationship in which the people involved are permitted or tolerated to be available to have additional simultaneous romantic and/or sexual relationships.

Wikipedia
Open relationship

An open relationship is an interpersonal relationship in which the parties want to be together but agree to a form of a non-monogamous relationship. This means that they agree that a romantic or intimate relationship with people hooking up with their partner is accepted, permitted, or tolerated. Generally, an open relationship is when the parties involved have two or more romantic or sexual relationships occurring at the same time either as a short-term relationship, such as dating, or a long-term relationship, such as marriage. The concept of an open relationship has been recognized since the 1970s.