  Magnetically tunable Feshbach resonances for polar paramagnetic ground-state
diatomics are too narrow to allow for magnetoassociation starting from trapped,
ultracold atoms. We show that non-resonant light can be used to engineer the
Feshbach resonances in their position and width. For non-resonant field
strengths of the order of $10^9\,$W/cm$^2$, we find the width to be increased
by three orders of magnitude, reaching a few Gauss. This opens the way for
producing ultracold molecules with sizeable electric and magnetic dipole
moments and thus for many-body quantum simulations with such particles.
