<p>A recently proposed addition to the holographic dictionary connects extremal black holes to fortuitous operators — those which are only supersymmetric for sufficiently small values of the central charge. The most efficient techniques for finding them come from studying the cohomology of a nilpotent supercharge. We explore two aspects of this problem in weakly-coupled ABJM theory, where the gauge group is U(<i>N</i>) × U(<i>N</i>) and the Chern-Simons level is taken to be large. Adapting an algorithm which has been used to great effect in 𝒩 = 4 Super Yang-Mills, we enumerate 244 low-lying fortuitous operators and sort them into multiplets of the centralizer algebra. This leads to the construction of two leading fortuitous representatives for <i>N</i> = 3 which are subleading for <i>N</i> = 2. In the second part of this work, we identify a truncation of ABJM theory where the action of the one-loop supercharge matches the one in the BMN subsector of 𝒩 = 4 Super Yang-Mills. This allows a known infinite tower of representatives to be lifted from one theory to the other.</p>