Is there a way to run Primitive+ servers?

yes, but keep in mind Prim+ is basically a hack of the game, masquerading as a mod. Each time the server starts, it has to load ARK, then unload ARK, then load all the Prim plus engrams. This mainly amounts to a vanilla server with one mod (Prim+ will not allow mods to load.) that takes 30 minutes + to start.

So any update of ARK or reboot will put you to a downtime.

Prim+ is SUPER fun, but it's much better as a solo or small group / tethered game experience.