  Three-body correlations, which arise between spin-polarized electrons in the
first excited Landau level, are believed to play a key role in the emergence of
enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent
advances in Floquet engineering, we investigate periodic driving of anisotropic
two-body interactions as a route for controllably creating and tuning effective
three-body interactions in the FQH regime. We develop an analytic formalism to
describe this Floquet-FQH protocol, which is distinct from previous approaches
that instead focus on bandstructure engineering via modulation of
single-particle hopping terms. By systematically analyzing the resulting
interactions using generalized pseudopotentials, we show that our Floquet-FQH
approach leads to repulsive as well as attractive three-body interactions that
are highly tunable and support a variety of non-Abelian multicomponent FQH
states. Finally, we propose an implementation of the protocol in optically
dressed ultracold polar molecules with modulated Rabi frequencies.
