The measurability of multiple quasinormal (QN) modes, including overtones and higher harmonics, with the Laser Interferometer Space Antenna is investigated by computing the gravitational wave (GW) signal induced by an intermediate or extreme mass ratio merger involving a supermassive black hole (SMBH). We confirm that the ringdown of rapidly spinning black holes are long-lived, and higher harmonics of the ringdown are significantly excited for mergers of small mass ratios.