We develop a technique to measure radial velocities of stars from spectra that present four sets of lines. The algorithm is an extension of the two-dimensional cross-correlation method TODCOR to four dimensions. It computes the correlation of the observed spectrum against a combination of four templates with all possible shifts, and it also allows for the derivation of the light ratios of the components. After testing the algorithm and demonstrating its ability to measure Doppler shifts accurately even under conditions of heavy line blending, we apply it to the case of the quadruple-lined system HD 110555. The primary and secondary components of this previously known visual binary ({rho}~0.4") are each shown to be double-lined spectroscopic binaries with periods of 57 days and 76 days, respectively, making the system a hierarchical quadruple. The secondary in the 76 days subsystem contributes only 2.5% to the total light, illustrating the ability of the method to measure velocities of very faint components.