There are many cesspool companies; to pump a cesspool, there is a flat fee plus a per-gallon fee for how many gallons they actually remove.
In northwestern Suffolk, AAA Cesspool is a good company. However, we never had to have ours pumped, so I have no idea how much they charge for that. We have had them do other things but not that.
https://www.aaacesspool.com
What makes you think that you need the cesspool pumped, by the way? Are you having backup issues? How long have you owned the house, and did you have the cesspool inspected before you bought it? (In other words, when was the last time you knew the condition of the cesspool.)