Lindner et al. [Phys. Rev. E 63, 051107 (2001)] have reported multiple stochastic resonances (SRs) in an array of underdamped monostable nonlinear oscillators. This is in contrast to the single SR observed earlier in a similar but isolated oscillator. Though the idea that such an effect might occur is intuitively reasonable, the notation and the interpretation of some of the major results seem confusing. These issues are identified and some of them are clarified. In addition, comments are made on two possible extensions of the central idea of Lindner et al.: one of these promises to provide much more striking manifestations of multiple SR in arrays; the other significantly widens the range of systems in which multiple SRs may be observed.