  We periodically modulate the lattice trapping potential of a $^{87}$Sr
optical clock to Floquet engineer the clock transition. In the context of
atomic gases in lattices, Floquet engineering has been used to shape the
dispersion and topology of Bloch quasi-energy bands. Differently from these
previous works manipulating the external (spatial) quasi-energies, we target
the internal atomic degrees of freedom. We shape Floquet spin quasi-energies
and measure their resonance profiles with Rabi spectroscopy. We provide the
spectroscopic sensitivity of each band by measuring the Fisher information and
show that this is not depleted by the Floquet dynamical modulation. The
demonstration that the internal degrees of freedom can be selectively
engineered by manipulating the external degrees of freedom inaugurates a novel
device with potential applications in metrology, sensing and quantum
simulations.
