If you would like to find out the total number of grievances, appeals and exception requests BlueCross BlueShield of South Carolina members have filed with us, please call our Member Services Department. BlueCross BlueShield of South Carolina members: Call 1-855-204-2744 (TTY 711). Hours are seven days a week, 8 a.m. to 8 p.m., Oct. 1 to Mar. 31. Monday – Friday, 8 a.m. to 8 p.m. all other times.