Sergeant Daniel Somers Network of Support Act This bill provides a means of disseminating information to personal contacts of Armed Forces members about the experiences and challenges of military service. Specifically, it requires the Department of Defense (DOD) to seek an agreement with the American Red Cross for the conduct of a pilot program to encourage new Armed Forces members to designate up to 15 persons with whom certain information regarding their military service would be shared. This includes information concerning aspects of daily life in the military and its challenges, particularly during and after deployment in a contingency operation; availability of services to help members and dependents to cope with experiences; and benefits provided by DOD. The bill provides privacy protections and mechanisms to modify the contact information or opt out of the program.