  Harvesting the full potential of black hole spectroscopy, demands realising
the importance of casting constraints on modified theories of gravity in a
framework as general and robust as possible. Requiring more stringent -- yet
well-motivated -- beyond General Relativity (GR) parametrizations,
substantially decreases the number of signals needed to detect a deviation from
GR predictions and increases the number of GR-violating coefficients that can
be constrained. To this end, we apply to LIGO-Virgo observations a high-spin
version of the Parametrized ringdown spin expansion coefficients (ParSpec)
formalism, encompassing large classes of modified theories of gravity. We
constrain the lowest-order perturbative deviation of the fundamental ringdown
frequency to be $\delta\omega^{0}_{220} = {-0.05}^{+0.05}_{-0.05}$, when
assuming adimensional beyond-GR couplings, substantially improving upon
previously published results. We also establish upper bounds $\ell_{p=2} < 23
\, \mathrm{km}$, $\ell_{p=4} < 35 \, \mathrm{km}$, $\ell_{p=6} < 42 \,
\mathrm{km}$ on the scale $\ell_p$ at which the appearance of new physics is
disfavoured, depending on the mass dimension $p$ of the ringdown coupling.
These bounds exceed the ones obtained by previous analyses or are competitive
with existing ones, depending on the specific alternative theory considered,
and promise to quickly improve as the number of detectors, sensitivity and
duty-cycle of the gravitational-wave network steadily increases.
