I also had this error message. A customer wants to bring two dogs - we charge extra for dogs/pets but I am getting this error - so cannot request payment.
I have not heard about customers splitting their payments (this is news to me). I think that as hosts we should be able to charge for these extra services at the point of booking - albeit that Airbnb schedule the request to the customer as and when full payment has been made. I now have to forward plan on my diary and "guess" when the full payment could made.
Can Airbnb look into a solution for this - it is not ideal at all.