They can't leave the scene of the accident (hit and run) -- so a different ambulance would be sent to the original call. The precedence of the original call is for "coming across" other cases, not causing them.
Most ambulances have limited space and that can make it difficult to pick up a second patient along the Way. But from a moral point of view I think it would be prudent to stop and pick up that person and take them to hospital
Our city's legal requirement is that a separate EMT unit must be dispatched for the new patient in order to ensure the safety and quick treatment of the first patient and for the safety of the first EMT vehicle and crew, nearby drivers/passengers in traffic, and bystanders/police/firefighters, at the second scene.
But morally, many of our EMT people want to be able to pick up the second patient as well. They can't risk their own patient and risk having an accident while helping the second patient, etc.
This applies only to my city and I don't know about other places.