We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in
N=4 super-Yang-Mills theory (SYM). Surprisingly, the
n-point
L-loop integrands with fixed
N:=n+L are unified in a single generating function. Similar to the SYM four-point half-BPS correlator integrand, the generating function enjoys a hidden
SN permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar
f-graphs. Remarkably, through Gram identities it can also be represented as a linear combination of bipartite
f-graphs which manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all
n with
N=4,6,8. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique
N=10 result, which provides new results for
n=10 squared tree amplitudes, as well as integrands for
(n,L)=(4,6),(6,4). Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.