We use K2 to continue the exploration of the distribution of rotation periods in Pleiades that we began in Paper I. We have discovered complicated multi-period behavior in Pleiades stars using these K2 data, and we have grouped them into categories, which are the focal part of this paper. About 24% of the sample has multiple, real frequencies in the periodogram, sometimes manifesting as obvious beating in the light curves. Those having complex and/or structured periodogram peaks, unresolved multiple periods, and resolved close multiple periods are likely due to spot/spot group evolution and/or latitudinal differential rotation; these largely compose the slowly rotating sequence in $P$ vs.~$(V-K_{rm s})_0$ identified in Paper I. The fast sequence in $P$ vs.~$(V-K_{rm s})_0$ is dominated by single-period stars; these are likely to be rotating as solid bodies. Paper III continues the discussion, speculating about the origin and evolution of the period distribution in the Pleiades.
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