  Over the past decade, the number of known wide binary systems has
exponentially expanded thanks to the release of data from the Gaia Mission.
Some of these wide binary systems are actually higher-order multiples, where
one of the components is an unresolved binary itself. One way to search for
these systems is by identifying overluminous components in the systems. In this
study, we examine 4947 K+K wide binary pairs from the SUPERWIDE catalog and
quantify the relative color and luminosity of the components to find evidence
for additional, unresolved companions. The method is best illustrated in a
graph we call the "Lobster diagram." To confirm that the identified
overluminous components are close binary systems, we cross-match our wide
binaries with the TESS, K2 and Kepler archives and search for the signs of
eclipses and fast stellar rotation modulation in the light curves. We find that
$78.9\%\pm20.7\%$ of the wide binaries which contain an eclipsing system are
identified to be overluminous in the "Lobster Diagram" and $73.5\%\pm12.4\%$ of
the wide binaries which contain a component showing fast rotation ($P<5$) days
also show an overluminous component. From these results, we calculate a revised
lower limit on the higher-order multiplicity fraction for K+K wide binaries of
$40.0\%\pm1.6\%$. We also examine the higher-order multiplicity fraction as a
function of projected physical separation and metallicity. The fraction is
unusually constant as a function of projected physical separation while we see
no statistically significant evidence that the fraction varies with
metallicity.
