Yes, depending on your city. Wheely offers a Designated driver service in Moscow and St. Petersburg.
When booking, select the Designated driver service level then specify your pickup location and destination. As with regular bookings, you can add a comment or book your chauffeur in advance.
Please see the price and conditions on the service level page for more information.
Please note: you will need a third-party vehicle insurance policy covering an unlimited number of guest drivers.