Circular stapling instruments and anvil assemblies. The anvil assemblies may have collapsible anvil support members that may be inserted through an opening in a patient and then expanded to be attached to an anvil plate assembly that has a staple-forming surface thereon. The anvil support member is attachable to the anvil plate assembly in such a way that when the anvil assembly is coupled to the stapling head of a circular stapler, the staple-forming surface is in substantial registry with the staples supported in the stapling head. A variety of different anvil support members and anvil plate assemblies are disclosed. Various embodiments have a tissue-piercing feature.