Lattice Monte Carlo simulations are used to study the stabilization of different ordered bicontinuous phases in A-B diblock copolymer systems. The stabilization approach involves attempting to reduce the packing, frustration inside the nodes of the bicontinuous phases by the addition of an A-component "additive". Two different strategies are considered which entail the addition of (1) explicit selective-solvent particles and (2) homopolymer of a length equal to 80% that of the diblock copolymer chains. Approximate phase boundaries were found via free-energy calculations, and great care was taken to enact the commensurability of system size with the unit-cell dimensions of distinct candidate phases. A very contrasting phase behavior is observed upon increasing the amount of the A-component additive in the two different strategies. With the first strategy (i.e., addition of solvent particles) we observed the progression gyroid --> perforated lamella --> lamella --> reversed gyroid, including a long-lived metastable orthorhombic cocontinuous phase known as O-52. With the second strategy (i.e., addition of homopolymer) we observed the progression of morphologies gyroid --> double diamond --> plumber's nightmare. In the latter two bicontinuous phases, the homopolymer concentrates preferentially in the nodes not only to reduce the nodal packing frustration but also to enhance the homopolymer's conformational entropy. At high homopolymer volume fractions, a novel morphology was observed, wherein cylinders of two different diameters alternate in a tetragonal (square) packing; however, it remains unclear whether this "alternating diameter cylinder" phase is just a long-lived metastable or a truly stable phase at some of the conditions examined. The dissimilarity in the resulting phase behavior for the two strategies considered is rationalized in terms of the difference in the degree of penetration of the two additives into the diblock copolymer layer, which is a direct consequence of the disparity in translational entropy exhibited by the homopolymers and by the solvent particles.