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We show that an iterative solution of rapidity evolution equations with a leading-order kernel renders the entire signature-odd tower of next-to-next-to-leading logarithmic (NNLL) contributions to partonic 2→2 amplitudes in the Regge limit computable in full color. The result, which universally holds in any gauge theory, corresponds to a set of three-Reggeon ladder diagrams. In this setting we compute the NNLL amplitude to four loops in dimensional regularization through finite corrections. Furthermore, by contrasting the result with the exponentiation properties of soft singularities we determine the four-loop correction to the soft anomalous dimension at this logarithmic accuracy. The latter features quartic Casimir contributions beyond those appearing in the cusp anomalous dimension. Finally, in the case of N=4 super Yang-Mills, we also determine the finite hard function at four loops through NNLL in full color.