© 2018 Optical Society of America. We introduce a simple scheme for mode-density multiplication of an optical frequency comb (OFC) by a factor of square of an arbitrary integer N using phase modulation. This scheme is employed to multiply the mode density of an erbium-doped fiber laser OFC (repetition rate of 66.87 MHz) by factors of 42, 82, and 3 · 42 using an electro-optic phase modulator. The OFC multiplied by 42 is applied to direct-comb spectroscopy of methane with a spectral resolution of 4.18 MHz.