You can receive new customer requests while you are busy with your present customer, but only when you are driving to the drop-off address. Apply for a new customer by clicking Yes on the order panel.
If you win the order, the message You are selected! Finish current order is shown.
Continue with your present customer. When you have dropped off your customer, tap Finish order. The route to your new customer is calculated and you can drive immediately to the pick-up location.
When you are not selected you see the message Sorry, you were not selected this time.