Is it possible to obtain an order for ultrasounds that is not limited to only one ultrasound so that a patient doesn't need to get a referral each time?

Yes: Ultrasounds often include multiple organs, so it should be possible. All the best.

Yes but depends : Ur dr can order an ultrasound to evaluate different organs but needs to have a specific diagnosis to justify each exam. Sometimes an ultrasound tech or radiologist finds something on an ultrasound and recommends another ultrasound in a few months to see if anything changed like an ovarian cyst or needs aspecial ultrasound like a sonohysyrerogram to get a better few of the uterus fot polyps.