We present a method of phase locking any number of continuous-wave lasers to an optical frequency comb (OFC) that enables independent frequency positioning and control of each laser while still maintaining lock to the OFC. The scheme employs an acousto-optic modulator (AOM) in a double-pass configuration added to each laser before its light is compared by optical heterodyne with the comb. The only requirement is that the tuning bandwidth of the double-pass AOM setup be larger than half the OFC repetition rate. We demonstrate this scheme and achieve an arbitrary frequency tuning precision, a tuning rate of 200 MHz/s, and a readout precision at the 1 kHz level.