In this Note, we present a dual-beam magneto-optical Kerr effect (MOKE) magnetometer for the study of quadratic MOKE in magnetic thin films. The two beams simultaneously probe the sample, located in the middle of a quadrupole magnet, at two angles of incidence (0 degrees and 45 degrees). This combination of two systems allows one to automatically and routinely perform measurements that are sensitive to the combined longitudinal and quadratic MOKE signals (45 degrees), or the quadratic effect alone (0 degrees). Orientation-dependent and automated quantitative analyses of the quadratic effect's amplitude are also implemented. We present representative measurements on Heusler compound thin films to illustrate the newly combined capabilities of this instrument.