Hi all! We are a mff poly relationship. 2 of us have been in a LTR, the third or us coming in just under 6 mo ago. We are all trying to navigate our relationship to the best of our abilities, and have come here looking for ways and ideas to make it strong, stable and lasting. Our f partner and I are very close, though her and I do not share a sexual relationship. We are essentially sister wives. Our m partner is still trying to find a good foothold to be able to juggle two very sexual females, work, and just life. Our f partner and I recently ordered the Ethical Slut, so we can read even more than my very thirsty brain has already researched, in an attempt to help us all. Help and a supportive community has been a miracle to find. We want to make this as easy as possible for us all. Any and all suggestions on articles, books, even what has worked for you are all welcome.
My suggestion is to not think of this as "one" relationship. In a triad, there are several relationships, in your case, thus:
You + F
M + F
M + You
F + You + M
Each dyad, even if nonsexual, needs to be nurtured separately. You need time carved out to hang out one-on-one, as well as spending time together as a threesome.
It's very important, if you live together, for each adult to have his or her own space, a bedroom or an office/studio. Everyone needs "me-time," as well as couple/triad time! Otherwise, you can start to get annoyed with each other.
You sound very enmeshed. You say "our" F partner, and things like that. It's fine to be individuals in a relationship. You're not a Star Trek Borg. "The most skipped step" article linked above addresses unhealthy entanglement, and how to disentangle for the health and longevity of the relationship(s).
It's up to each individual to satisfy themselves sexually. However, if your man can't keep up with your sexual appetites, he could buy you a nice vibrator.

(Of course, you can buy one for yourself.) Or you could seek another partner (or two) to have sex with. I'm poly, but even when I had up to 3-4 partners at a time, I still masturbated regularly. People aren't sex toasters. You can't just expect toast any time you want.
If your man needs more alone time, or time for work, family, hobbies, other friends, etc., it's up to him to set aside time for all of that. Romantic relationships should not be all-consuming. If he doesn't have time in his week to fully take care of all the areas, something needs to go. Maybe he's not cut out for polyamory at this time in his life. Or maybe his gfs could be less demanding, and give him some space. He's just one guy.