Monogamish
A largely-monogamous relationship that has agreed-on, often narrow, exceptions to strict exclusivity — typically rare, usually sexual, often situational.
The term monogamish was coined by sex-advice columnist Dan Savage to describe relationships that are predominantly monogamous but include explicit, negotiated exceptions. The exceptions tend to be narrow: a 'one-night rule' while travelling separately, a yearly negotiated allowance, sex with one specific other person under specific conditions, attendance at a particular event together. The default is exclusivity; the exceptions are the noteworthy part.
Monogamish differs from open relationships in scale and frequency. An open relationship treats outside connections as part of the ongoing structure; a monogamish arrangement treats them as exceptions to a baseline. Monogamish differs from polyamory because the romantic-partnership identity stays singular: the monogamish couple are a couple, full stop, who occasionally sleep with other people on agreed terms.
Why couples land on monogamish rather than full openness: it preserves most of the familiar shape and most of the social legibility of monogamy while creating room for specific desires (often around travel, around a particular friend, around a long-running fantasy) without requiring the much larger structural changes a fully open or polyamorous arrangement entails.
Risks specific to monogamish arrangements include exception-creep (the agreed-rare exception becomes routine, and the structure has not been re-negotiated to reflect the new reality), and disclosure ambiguity (whether the partner is told before, after, or about specific encounters at all). The healthier monogamish arrangements have a clear protocol for the exceptions and clear conditions under which the structure would be re-opened for negotiation.