  Two-loop MHV amplitudes in planar ${\cal N} = 4$ supersymmetric Yang Mills
theory are known to exhibit many intriguing forms of cluster-algebraic
structure. We leverage this structure to upgrade the symbols of the eight- and
nine-particle amplitudes to complete analytic functions. This is done by
systematically projecting onto the components of these amplitudes that take
different functional forms, and matching each component to an ansatz of
multiple polylogarithms with negative cluster-coordinate arguments. The
remaining additive constant can be determined analytically by comparing the
collinear limit of each amplitude to known lower-multiplicity results. We also
observe that the nonclassical part of each of these amplitudes admits a unique
decomposition in terms of a specific $A_3$ cluster polylogarithm, and explore
the numerical behavior of the remainder function along lines in the positive
region.
