  Controlled modifications of the quantum magnetic response are produced in
dressed systems by a high frequency, strong and not-resonant electromagnetic
field. This quantum control is greatly enhanced and enriched by the harmonic,
commensurable and orthogonally oriented dual dressing theoretically discussed
here. The secondary field enables a fine tuning of the qubit response, with
control parameters amplitude, harmonic content, spatial orientation and phase
relation. Our analysis is based on a perturbative approach and includes few
numerical solutions. The long-time dynamics is described in terms of an
anisotropic effective static magnetic field representing the handle for the
system full engineering. Through a low-order harmonic mixing the bichromatic
driving generates a rectified static field acting on the spin. The Zeeman
response becomes anisotropic in a triaxial geometry and includes a quadratic
contribution. Our dressing increases the two-level energy splitting, improving
the spin detection sensitivity. On the low field direction it compensates the
static fields applied in different geometries. A resonant spin exchange between
two species having very different magnetic response as electron and nucleus is
allowed by the dressing. The spin temporal evolution includes a micromotion at
harmonics of the driving frequency whose role in the spin detection is examined
and can be exploited in quantum information. The results presented here lay a
foundation for additional applications to be harnessed in quantum simulations.
