A cyclic method of chemical mechanical polishing (CMP) a wafer having a surface includes placing the wafer on a platen in a CMP apparatus and then performing a multi-step CMP comprising process. The multi-step CMP process includes delivering a first chemical composition onto the wafer while on the platen for a first time duration, and without removing the wafer from the platen, delivering a second chemical composition different from the first composition onto the wafer for a second time duration after the first time duration. The multi-step CMP comprising process includes CMP removal using a slurry during one of the first and second time durations and a non-polishing process during the other of the first and second time durations. The multi-step CMP comprising process is repeated a plurality of times.