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Optical-optical double-resonance spectroscopy with a continuous wave pump and frequency comb probe allows measurement of sub-Doppler transitions to highly excited molecular states over a wide spectral range with high frequency accuracy. We report on assessment and characterization of sub-Doppler double-resonance transitions in methane measured using a 3.3-μm continuous wave optical parametric oscillator as a pump and a 1.67-μm frequency comb as a probe. The comb spectra were recorded using a Fourier transform spectrometer with comb-mode-limited resolution. With the pump tuned to nine different transitions in the ν3 fundamental band, we detected 36 ladder-type transitions to the 3ν3 overtone band region, and 18 V-type transitions to the 2ν3 overtone band. We describe in detail the experimental approach and the pump stabilization scheme, which currently limits the frequency accuracy of the measurement. We present the data analysis procedure used to extract the frequencies and intensities of the probe transitions for parallel and perpendicular relative pump-probe polarization. We compare the center frequencies and relative intensities of the ladder-type transitions to theoretical predictions from the TheoReTS and ExoMol line lists, demonstrating good agreement with TheoReTS.