  We examine in detail the structure of the Regge limit of the (nonplanar)
${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color
factors $C_{ik}$ suitable for the Regge limit of the amplitude at any loop
order, and then calculate explicitly the coefficients of the amplitude in that
basis through three-loop order using the Regge limit of the full amplitude
previously calculated by Henn and Mistlberger. We compute these coefficients
exactly at one loop, through ${\cal O} (\epsilon^2)$ at two loops, and through
${\cal O} (\epsilon^0)$ at three loops, verifying that the IR-divergent pieces
are consistent with (the Regge limit of) the expected infrared divergence
structure, including a contribution from the three-loop correction to the
dipole formula. We also verify consistency with the IR-finite NLL and NNLL
predictions of Caron-Huot et al. Finally we use these results to motivate the
conjecture of an all-orders relation between one of the coefficients and the
Regge limit of the ${\cal N} =8$ supergravity four-point amplitude.
