  In a previous paper, using data from K2 Campaign 2, we identified 11 very low
mass members of the $\rho$ Oph and Upper Scorpius star-forming region as having
periodic photometric variability and phased light curves showing multiple
scallops or undulations. All the stars with the "scallop-shell" light curve
morphology are mid-to-late M dwarfs without evidence of active accretion, and
with photometric periods generally $<$1 day. Their phased light curves have too
much structure to be attributed to non-axisymmetrically distributed
photospheric spots and rotational modulation. We have now identified an
additional eight probable members of the same star-forming region plus three
stars in the Taurus star-forming region with this same light curve morphology
and sharing the same period and spectral type range as the previous group. We
describe the light curves of these new stars in detail and present their
general physical characteristics. We also examine the properties of the overall
set of stars in order to identify common features that might help elucidate the
causes of their photometric variability.
