Family Medicine Care on Demand Clinic. 1801 Briarwood Circle Building 10. Ann Arbor, MI 48108. 734-998-6649. Saturday only, 11a.m. - 5 p.m. U-M Family Medicine offers Care on Demand hours for ALL U-M Family Medicine patients. At this time, the care team are unable to treat individuals who do not currently see a U-M Family Medicine primary care ....