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We present an optical-optical double-resonance (OODR) spectrometer based on a 3.3 µm continuous wave pump and two cavity-enhanced probes: a frequency comb tunable in the 1.64–1.8 µm range, and a comb-referenced continuous wave (CW) laser tunable in the 1.6–1.75 µm range. The comb probe provides broad spectral coverage (bandwidth up to 7 THz) for simultaneous detection of many sub-Doppler OODR transitions with sub-MHz line position accuracy, while the CW probe allows targeting individual transitions with kHz accuracy and a higher signal-to-noise ratio in shorter time. Using the pump stabilized to the frequency of the R(0) transition in the v₃ band of methane and the comb probe covering the 5550 to 6070 cm⁻¹ interval, we detect 37 ladder-type transitions in the 3v₃ ← v₃ band region and 6 V-type transitions in the 2v₃ band region and assign them using available theoretical predictions. Using the CW probe, we measure selected ladder- and V-type transitions with much higher precision. We also detect Lamb dips in the R(0) – R(3) transitions of the 2v₃ band and report their center frequencies with kHz-level accuracy. The synergy effects of the comb- and CW-OODR open new possibilities in precision spectroscopy of levels that cannot be reached from the ground state.