You are not owned by Airbnb, so you can make any arrangements with guests that you want, except for circumventing Airbnb for their initial booking.
Of course the guest wants to do this, as he will save the service charges. But you won't be covered, supported or protected in any way should you find the guest has suddenly invited 3 more family members to your home, or you find the space trashed out or things destroyed or broken. I would personally never agree to this with a guest who has only stayed for 2 nights or who you have not had a very positive and personal interaction with.
I have had guests who stayed for 10 days or 2 weeks, they were lovely, respectful people who left the place immaculate, we really connected and became friends- those people are welcome to contact me privately if they ever want to stay again. But just a regular Airbnb guest who wanted to extend a short reservation off-platform, no way.