Recent advances in generation of strong laser pulses have enabled the acceleration of electrons in solids into regions far away from the band edge. Because nonlinear currents can be generated by laser-driven carriers in the non-parabolic region, tailored laser fields may allow control of optical properties of high-order harmonics (HHs). So far, investigations on laser-induced nonlinear optical phenomena have focused on the simple electron motion induced by linearly or elliptically polarized fields. However, more complex trajectories can be important for development of novel optoelectronic devices. Here, we show that a weak laser field (optical frequency is ω2) applied in a direction orthogonal to a strong main field (ω1) enhances certain HH intensity components of bulk GaSe by a factor of 100. Good agreement between the experiments and calculations shows that manipulation of the electron trajectory allows breaking inversion symmetry of the electronic states felt by the accelerated electrons and leading to a modification of selection rules for frequency-mixing processes of HHs. Owing to our usage of non-integer multiples for ω1 and ω2, it is found that the generation of HHs constitutes a novel way of ultrafast control of light polarization and optical switching.