SIAP Can one arrange to have a single Uber driver on a regular basis (off-peak hours only)

We are a couple of really, really old people moving from a small town in SW France to Austin TX. We would prefer using one or two Uber luxury car drivers frequently as we will not buy a car. Virtually all of our traveling will be off-peak within the city limits with rides ranging from a mile to 30 miles each way. Is it possible to make an arrangement with one or two or three drivers that we could us on an repeated basis? Thanks