It's always difficult @MaryLynne--Mel-0 - if people are determined to break rules they can often find a way.
I am a remote host and my lsiting can sleep up to 8, so I am a prime target for this kind of behaviour.
I have a raft of strategies in place to try to ensure people who are planning to sneak in extras don't bother booking with me. Nothing's foolproof, but I find the following helpful
I state I will be there to check in the guest ( ie I dont' advertise I have self check in, even though it's possible). I have stated exterior surveillance, and I have a substantial security deposit. ( the deposit is pretty useless and airbnb dont' even hold it on your behalf, but a lot of guests don't KNOW that, so it's good for bluff value)
In my house rules I say something along the lines of 'Only the guests nominated on the booking may stay at the house. this includes visitors. This is an insurance requirement. Guests violating this rule will have their bookings cancelled
within the house rules I also have a code word
I have IB so I have a pre booking message - in that I ask guests to prove they've read the house rules by quoting the hidden code word.-
And finally after a guest has booked I request that they enter the full legal names of every guest coming including children, stating that it is an insurance requirement ( which it is for me) I further state if more peopel are coming, they need to be added to the booking and extra charges will apply
If I get a booking for 2 adults only, I would lock off the extra bedrooms. (I say this in the description and state it is to minimise excess linen charges)
It all sounds like a lot of work, but most of it I have in place already.
People quickly get the idea that sneaking people in isn't worth the effort.
Of course there are also some guests who genuinely misunderstand and think that if a listing sleeps 3, they can bring 3, even if they've only paid for 1. Airbnb isn't very good at explaining this, adn some listings make their base rate for the maximum number of guests, so there's not consistency and it IS easy to make a genuine mistake.
Since I"ve done all that, I've been much happier with the guests who have booked.
Hope this helps a bit.
Cheers