adj. In a monogamous relationship, but with a mutual agreement that allows occasional infidelities.
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Personally, I'm in a monogamish relationship. We're committed to each other, but have a porous boundary around our relationship, meaning we've agreed that it's OK for either of us to express romantic feelings toward other people or to be physically intimate with other people, so long as we're honest and transparent about our intentions with one another.
—Chris Messina, “Why I choose non-monogamy,” CNN Money, January 29, 2015
The idea that monogamy "is a social expectation but not a biological reality," as the survey put it, was true for more than half of all the Gen X and Y respondents. (The survey apparently didn’t ask if it was neither of those, but a learned skill, like, say, reading, gymnastics or coding.) But somewhat surprisingly, only one in five men preferred the idea of what could be called a "monogamish" relationship — where people are mostly faithful — over a monogamous one.
—Belinda Luscombe, “Are You ‘Monogamish’? A New Survey Says Lots of Couples Are,” Time, July 17, 2014
So I've got a new word to describe relationships like yours, mine, and your mom's, IIC: "monogamish." We're mostly monogamous, not swingers, not actively looking. Monogamish.
—Dan Savage, “Savage Love: Monogamish,” The Stranger, July 20, 2011
2010 (earliest)
monogamish: A relationship that is mostly monogamous but occasionally exceptions are made for sexual play.
—sluttychica, “monogamish,” Urban Dictionary, August 17, 2010
Many thanks to Alan Bardsley for spying this term.