We did a combination of what most of the girls did/planning on doing..
We filled in the name(s) of the invited guest(s) on the RSVP cards. A few of our friends who we knew were in a relationship but did not know their gf/bf name, I wrapped a belly band around the RSVP card and told them they were welcome to bring a
guest.
Having done the above we still received RSVP cards back where guests added someone to them (a couple was already allowed to bring one guest) - DH and I returned those phone calls (he called his friends and I called mine - Most was mainly his
friends) letting them know that we were limited due to accomodations and budget. (You MUST say due to accommodation and budget) when we would say due to budget, we had folks offering to pay for their guests.
We only had one single gm and we allowed him to bring a guest. He wanted to bring some girl he just me but he didn't. (I didn't understand why he would have wanted to anyway).