Interactions between aqueous fluids and clay-containing subterranean formations may be problematic due to issues associated with clay destabilization and migration. Subterranean treatment methods may comprise: providing a clay stabilizing composition comprising an amine-functionalized dextrin compound having 2 to about 20 glucose units linked together with α(1,4) glycosidic bonds, and an amine-functionalized dextran polymer having a plurality of glucose units linked together with α(1,6) glycosidic bonds; introducing the clay stabilizing composition into a subterranean formation bearing a clay-containing mineral; and interacting the amine-functionalized dextrin compound and the amine-functionalized dextran polymer with the clay-containing mineral to affect stabilization thereof. A portion of the glucose units are oxidatively opened and functionalized with at least one amine group at a site of oxidative opening in both the amine-functionalized dextrin compound and the amine-functionalized dextran polymer. The amine-functionalized dextrin compound and the amine-functionalized dextran polymer operate synergistically with one another.