Monogamish
Monogamish describes a mostly monogamous couple who allow occasional, agreed-upon sexual experiences outside the relationship.

Monogamish is a term for couples who are largely monogamous but leave a little room — by mutual agreement — for occasional sexual experiences with others. Popularised by advice columnist Dan Savage, it captures a middle ground between strict exclusivity and a fully open arrangement.
What counts as "occasional" is defined entirely by the couple: a pass while travelling, the freedom to flirt or play at a party, or a rare third for a special night. The relationship stays the clear centre, with outside experiences treated as exceptions rather than a lifestyle.
Like every form of ethical non-monogamy, monogamish works on honesty and clear boundaries. Couples tend to set simple, well-understood rules and check in often, keeping the emphasis firmly on their primary bond.
Frequently asked
It is a lighter version. Open relationships build in ongoing outside connections; monogamish couples allow only occasional, exceptional ones.
It was popularised by advice columnist Dan Savage to describe mostly-monogamous couples with a little agreed flexibility.