While the third harmonic of a monochromatic pump field with a frequency omega0 is generated exactly at the frequency 3omega0, frequency tripling of broadband ultrashort pump pulses in extended nonlinear media tends to generate isolated spectral peaks substantially shifted from 3omega0. We demonstrate this phenomenon by studying nonlinear spectral transformations of femtosecond Cr:forsterite laser pulses in multimode photonic-crystal fibers. Third-harmonic generation is shown to map adjacent guided modes of the third harmonic onto a manifold of spectral peaks within a 150-THz range around 3omega0. The spectral shifts and the widths of these peaks are controlled by the phase and group-velocity mismatch between the pump field and third-harmonic modes, as well as the length of nonlinear-optical interaction and broadening of the pump spectrum, allowing the spectral content of the third-harmonic signal to be engineered by tailoring the fiber dispersion.