Along the same line as an appointment scheduler, you can open an answering service. What you will do is take after hour calls for businesses. This can be a bit harder depending on what you offer your clients.
You can simply offer to take messages and deliver them immediately if they are urgent or you can work as a customer service line where you answer questions and help customers. The extent of your answering service would depend upon your abilities to help customers.
Most commonly answering services are used by doctors. Patient’s call after hours with emergencies or questions that need answers before the next day of business. You take the call and page the doctor who then calls the patient back. There may be possibilities for other types of businesses too. Ask around and see what interest there is in such a service.