I'm going to give some different advice here:
It sounds like this guy is no longer meeting your needs or making you happy. You should break up with him.
If you eventually find a primary of your own and feel like your life would be more enriched by having the first guy as a secondary again, you could try getting back together with him then.
But right now, it sounds like seeing this guy once a week is making you feel MORE lonely and unfulfilled than you would if you were fully single.
Change what you two do on your once-a-week night together. Go out places and talk more rather than just having him come over for a sleepless night of hot sex (if that's largely what's happening).
Change your attitude so that you identify as single-and-seeking-a-primary-partner (like tons of people, both mono and poly). Put effort into dating and meeting new people. Then, if you feel like being a secondary to this guy once a week will still be fun and enriching, you can keep doing it while you are also dating other people.
My own attitude is the opposite of yours--I don't want a primary partner and I would be happy to be someone's secondary. I need a lot of alone time. The energy, time, and passion that other people put into a primary relationship, I put into my writing. I consider myself my own primary--and I think that's awesome and it makes me really happy.
I find it irritating having a boyfriend involved with my daily life. And I would never inflict my dull office Christmas party on anyone I was dating!
But it sounds like the dynamic works best for your boyfriend if his secondary girlfriends have primaries of their own.
Single, straight, female, solo, non-monogamous.