Is it possible to adjust pricing after service is rendered for house sitting?

I'm wondering if after booking with a client for a house-sit and agreeing on a price depending on time frame that was given pre-book, can you change or adjust the amount for services rendered after booking? Like for example should they come back later than agreed upon. I hope this makes sense.. I guess what I'm really asking is if there is a way to add or adjust the price for your visit AFTER the services have been provided and booked? And would this be reasonable to do if your client comes back late or asks you to stay longer than anticipated?