A composition and an associated method for chemical mechanical planarization (or other polishing) are described. The composition includes a surface-modified abrasive modified with at least one stabilizer and at least one catalyst differing from the at least one stabilizer. The composition can further include a medium containing the abrasive and an oxidizing agent (e.g., hydrogen peroxide), wherein the at least one catalyst is adapted to catalyze oxidation of a substrate by the oxidizing agent. Preferably, the abrasive is alumina, titania, zirconia, germania, silica, ceria and/or mixtures thereof, the stabilizer is B, W and/or Al, and the catalyst is Cu, Fe, Mn, Ti, W and/or V. Both the stabilizer and the catalyst are immobilized on the abrasive surface. The method includes applying the composition to a substrate to be polished, such as substrates containing W, Cu and/or dielectrics.