Does the building's doorman deserve additional pay if he washes the car more than once a week, considering the prior agreement was to wash it once a week for a specific amount?

The contract is the law between the contracting parties. As long as the agreement is to wash the car once a week, there is no obligation to pay more if he washes it more often, because he is doing so voluntarily. However, if you wish to show kindness to him, that would be good, for Allah Almighty says: "Is the reward for good [anything] but good?"