  In 1988, George Andrews and Frank Garvan discovered a crank for $p(n)$. In
2020, Larry Rolen, Zack Tripp, and Ian Wagner generalized the crank for p(n) in
order to accommodate Ramanujan-like congruences for $k$-colored partitions. In
this paper, we utilize the techniques used by Rolen, Tripp, and Wagner for
crank generating functions in order to define a crank generating function for
$(k + j)$-colored partitions where $j$ colors have distinct parts. We provide
three infinite families of crank generating functions and conjecture a general
crank generating function for such partitions.
