Connect with users on a more personal and helpful level. Create a "Ask a doc" campaign on Facebook where Blue Shield teams up with new and veteran MDs and let the users ask general questions. Respond in quick video format within 10-20 minutes of the question. This really hits that blue shield is NOT FOR PROFIT, offering a personal service for free on the internet asking nothing in return.
Create a character who is a doctor that goes through the entire internet and finds people complaining about their medical problems and give them direct advice in a video reply. It's like Batman in a way, just crawling the internet and helping people that are otherwise getting bad or no advice from places like Yahoo Answers, Youtube, reddit's /r/health/ section, etc.