The appearance of nonlinearity in multiphonon excitations is compared in the series of [Pt(en)(2)X-2][Pt(en)(2)](ClO4)(4) (X = Cl, Br, I; en = ethylenediamine) mixed-valence, linear-chain, charge-density-wave compounds. This comparison is made for crystals obtained under new synthetic conditions that minimize chemical defects incorporated during crystal growth. The single-crystal resonance Raman spectra collected at 77 K on this series (with natural isotope abundances) show strong red-shifting of the X-Pt-X symmetric stretch overtone peaks for X = Cl, modest red-shifting for X = Br, and no anharmonicity for X = I. When X = Cl, by the sixth overtone of the Cl-35-Pt-Cl-35 stretch, red shifts significantly larger than 10% of the fundamental frequency are observed. In addition, evolution of spectral line shapes corresponding to formation of dynamically localized vibrational states (intrinsically localized modes) is apparent, even by the second overtone. When X = Br, observed red shifts are less than 7% up to the eighth overtone, and there is no spectral evidence for intrinsically localized modes at 77 K. Further study of X = Br at 4 K yields spectra up to the 11th overtone having similar red shifts and narrower line shapes than at 77 K but provides only very ambiguous indications of resolved combination bands that could correspond to intrinsically localized modes. When X = 1, the lack of any observed anharmonicity indicates linear phonon excitations, which likely correspond to highly delocalized small amplitude motions. The series of data presented here demonstrate how nonlinearities in vibrational degrees of freedom, and the corresponding existence of localized modes, can be tuned chemically by adjusting the competing effects of electron delocalization and electron-phonon interactions in low-dimensional materials.