For enterprises, customer relationships have been well recognized as a critical factor to succeed their business. To address this trend, Consumer Support System (CSS) is proposed that emphasizes on collecting customer information (i.e., knowledge from customers) for enterprises to catch customer needs and then based on these needs delivering services to benefit customers. Although CSS has considered both directions of the work flows between enterprises and customers, it however does not employ such well-known social features as social collaborative business among enterprises and customers to create more customer values and also social business process management to promote business processes. For this need, we present in this paper a discussion, namely Social Customer Support System (SCSS), that extends CSS with these social features. The discussion figures out a SCSS architecture with necessary components and management mechanisms to encompass the social features in SCSS.