Hey Simon, welcome to the community!
That's odd. All family plans are able to invite up to 5 additional accounts.
For all the information on how to manage your Premium for Family plan, check this support page.
If you're still missing an invite, try taking a screenshot and sending it over.
We'll take a closer look.
“Music acts like a magic key, to which the most tightly closed heart opens.”
― Maria Augusta von Trapp