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We present two series of MOST (Microvariability and Oscillations of STars) space-based photometry, covering nearly continuously 10 d in 2004 and 30 d in 2007, of selected variable stars in the upper main sequence of the old open cluster M67. New high-precision light curves were obtained for the blue straggler binary/triple systems AH Cnc, ES Cnc and EV Cnc. The precision and phase coverage of ES Cnc and EV Cnc is by far superior to any previous observations. The light curve of ES Cnc is modelled in detail, assuming two dark photospheric spots and Roche geometry. An analysis of the light curve of AH Cnc indicates a low mass ratio (q ∼ 0.13) and a high inclination angle for this system. Two new long-period eclipsing binaries, GSC 814-323 and HD 75638 (non-members of M67) were discovered. We also present ground-based DDO spectroscopy of ES Cnc and of the newly found eclipsing binaries. Especially interesting is HD 75638, a member of a visual binary, which must itself be a triple or a higher multiplicity system. New light curves of two δ Scuti pulsators, EX Cnc and EW Cnc, have been analysed leading to detection of 26 and eight pulsation frequencies of high temporal stability.