MultiCare Allenmore Hospital, 253-459-6200. MultiCare Auburn Medical Center, 253-833-7711. MultiCare Capital Medical Center, 360-754-5858. MultiCare Covington Medical Center, 253-372-6500. MultiCare Deaconess Hospital, 509-473-5800. MultiCare Good Samaritan Hospital, 253-697-4000. MultiCare Tacoma General Hospital, 253-403-1000..