The Inverse Seesaw mechanism remains one of the most attractive explanations for the lightness of neutrino masses, allowing for natural low-scale realisations. We consider the prospects of a simple extension via 3 generations of sterile fermions - the so called ISS(3,3) - in what concerns numerous lepton flavour observables. In order to facilitate a connection between the Lagrangian parameters and low-energy data, we systematically develop new parametrisations of the Yukawa couplings. Relying on these new parametrisations to explore the parameter space, we discuss the complementary role of charged lepton flavour violation searches in dedicated facilities, as well as in lepton colliders (FCC-ee and $\mu$TRISTAN). Our results reveal the strong synergy of the different indirect searches in probing the distinct flavour sectors of the model. In particular, we show that in the absence of radiative decays $\ell_\alpha\to\ell_\beta\gamma$, sizeable rates for $Z$-penguin dominated observables could hint at a non-trivially mixed and non-degenerate heavy spectrum.