In this work, a novel kind of interesting spectral change, multiple spectral switches, is revealed for the first time. During the analysis of the evolution of the scattered spectrum for a newly proposed electromagnetic random source of circular frame upon a semisoft boundary medium in the far zone, it is shown that, with appropriate system parameters, the scattered spectrum would present a unique double-peak configuration, which is the well-known spectral switch. When further increase the scattering angle, to our great surprise, the spectral switches may repeat several times, which effect we define multiple spectral switches. In addition, influence of several parameters such as the incident light beam order M, the semisoft boundary summation index N, and the effective width σ R of the medium on the spectral switch are discussed in detail. Results obtained here may further enrich the scattering theory, and find applications in obtaining the structure information of the scattering objects, in the search of particular spectral lines in astronomy, or to develop spectrum-selective optical interconnects in optical computing.