Over the years I've had a variety of relationships where the woman was sexually/romantically exclusive to me, but not I to her.
I learned the techniques to set up and manage relationships like this from an old instructor of mine, who'd often maintain 5-7 girlfriends at once, with 2-3 of them as serious relationships.
This was a lot more common in the early days of the seduction community. Men called them 'mLTRs' then (short for 'multiple long-term relationships'). Many of the guys running mLTRs didn't ask for (or weren't able to get) exclusivity from their girls. But some of them did.
Because pretty much all my romantic experience came post-discovering the seduction community, I dove right in, and went into setting up mLTRs from my very first relationships. I was a young dumb kid, dating women who were a lot more experienced than he was, and I figured it wouldn't work and I'd get laughed out of these girls' apartments and lives... but to my surprise, it did.
I've tended to call this setup 'one-sided monogamy' when I've mentioned it on this site. But since I'm talking about it here, I've realized this term, while descriptive, doesn't sound great, and doesn't really do the relationship justice. (while only one party is monogamous, the relationship itself is not 'one-sided')
So for this piece, we'll just call these women you have in a relationship like this 'consorts' or 'mistresses'.