The addition of a third component to a binary mixture usually alters the critical temperature and critical composition for phase separation. In practice, these shifts can be large, leading to both increasing and decreasing of the phase stability of the mixture. Lattice cluster theory calculations show that the addition of a small amount of A-b-B diblock copolymer to an A/B polymer blend shifts the phase boundary as "impurities" do in other fluid mixtures. The novel feature associated with the dilution of the blend by a diblock. copolymer additive is that both stabilization and destabilization can be achieved for certain conditions merely by "tuning" the asymmetry of the block lengths in the diblock copolymer. More substantial shifts are found in the phase diagram of a blend [polystyrene/poly(vinyl methyl ether)] exhibiting a lower critical solution temperature. We also examine the relation between the shifts in the critical temperature and in the critical composition of the blend in order to compare with a phenomenological relation which is observed to apply for small molecule diluted mixtures. The shift of the; critical temperature is found to be approximately linearly related to the critical composition shift when the block copolymer is nearly symmetric, but no simple relation seems to exist for asymmetric diblock copolymers.