Two-color second-order correlations of the light scattered near-resonantly by a quantum dot were measured by means of spectrally-filtered coincidence detection. The effects of filter frequency and bandwidth were studied under monochromatic laser excitation, and a complete two-photon spectrum was reconstructed. In contrast to the ordinary one-photon spectrum, the two-photon spectrum is asymmetric with laser detuning and exhibits a rich structure associated with both real and virtual two-photon transitions down the dressed states ladder. Photon pairs generated via virtual transitions are found to violate the Cauchy-Schwartz inequality by a factor of 60. Our experiments are well described by the theoretical expressions obtained by del Valle et al. via time-and normally-ordered correlation functions.