The two-photon dressing of a "three-level ladder" system, here the ground state, the exciton, and the biexciton of a semiconductor quantum dot, leads to new eigenstates and allows one to manipulate the time ordering of the paired photons without unitary postprocessing. We show that, after spectral postselection of the single dressed states, the time ordering of the cascaded photons can be removed or conserved. Our joint experimental and theoretical study demonstrates the high potential of a "ladder" system to be a versatile source of orthogonally polarized, bunched or antibunched pairs of photons.