I think the biggest problem you face with this idea is that open invites and formal invites are two very different things, and you're trying to combine them.
If you truly want people to bring along everyone they've ever known, that's never going to be something I consider negative. Generosity and open-heartedness are great qualities. I'm all for them.
Alas, opening up the guest list to such a complete free-for-all immediately indicates to guests that they don't actually have to say whether they're coming and how many people they're bringing. It's hard enough to get people to respond when the invitiation is very clear about who is and isn't invited and begs for a reply by a certain date. If the invitation gives the same impression as a college kegger, then you're going to get even less replies.
There is no correct wording for this in place because in most cases people are either inviting people to appear randomly and bring all their friends OR they issue formal invitations.
I'm not saying it can't be done, but I will tell you it's going to confuse a lot of people because it's neither fish nor fowl and folks haven't run across anything quite like it before.
So if this is truly what you want to do (and it's your day, so if you really want your second-cousin's third-grade teaching assistant to show up, then who am I to argue?), then you're going to have to a) come up with a wording of your own AND b) be prepared to call your entire formally-invited list to find out whether they're coming and whom they plan to bring with them.
I'd recommend something along the lines of: the better to share our joy, we invite you to bring as many guests as you please. RSVP with complete number of party by x date.
Then be ready with the phone list the day after x date so you can plan enough food and chairs.