We present an extension of the model proposed recently to account for dramatic changes below T c (anomalies) of some c-axis polarized infrared-active phonons in bilayer cuprate superconductors, that applies to trilayer high-T c compounds. We discuss several types of phonon anomalies that can occur in these systems and demonstrate that our model is capable of explaining the spectral changes occurring upon entering the superconducting state in the trilayer compound Tl 2 Ba 2 Ca 2 Cu 3 O 10 . The low-temperature spectra of this compound obtained by Zetterer and coworkers display an additional broad absorption band, similar to the one observed in underdoped YBa 2 Cu 3 O 7−δ and Bi 2 Sr 2 CaCu 2 O 8 . In addition, three phonon modes are strongly anomalous. We attribute the absorption band to the transverse Josephson plasma resonance, similar to that of the bilayer compounds. The phonon anomalies are shown to result from a modification of the local fields induced by the formation of the resonance. The spectral changes in Tl 2 Ba 2 Ca 2 Cu 3 O 10 are compared with those occurring in Bi 2 Sr 2 Ca 2 Cu 3 O 10 , reported recently by Boris and coworkers.