We report on high-order magnetoplasmon resonances detected in photoresistance in high-mobility GaAs quantum wells. These resonances manifest themselves as a series of photoresistance extrema in the regime of Shubnikov-de Haas oscillations. Extending to orders above 20, the extrema exhibit alternating strength, being less (more) pronounced at even (odd) order magnetoplasmon modes. This experimental technique provides sensitive and elegant means to detect and investigate multiple magnetoplasmon modes and could be applied to other systems.