A method of fabricating a monolithic honeycomb structure product involves shaping a first mixture of raw materials and a binder into a green honeycomb, extruding a second mixture of raw materials and a binder into one or more green members that each define an opening extending longitudinally therethrough. The raw materials of the second mixture are compatible with the raw materials of the first mixture. The green honeycomb and member(s) are dried. The binders of the green honeycomb and member(s) are softened at the surfaces that are to be bonded. The green member(s) is inserted into the honeycomb and bonded to the honeycomb to form an assembly thereof, which is then dried and fired to form a unified monolithic honeycomb structure. The insertion is best carried out by mounting a member in the shape of a tube on a mandrel, and inserting the mandrel into the honeycomb opening to bond the tube to the honeycomb.