<p>The Richtmyer-Meshkov instability on a single-mode interface subjected to sequential co- and counter-directional reshocks is investigated through shock-tube experiments and theoretical analysis. Models describing the complete evolution of the single-shocked interface and the double-shocked interface following a co-directional reshock are first developed, which demonstrate favourable predictive capability for the experimental measurements. However, a straightforward extension of these models to a triple-shocked interface subjected to a counter-directional reshock proves inadequate, owing to the insufficient characterization of the secondary-compression and wavelength-asymmetry effects. By introducing physically motivated parameters that precisely account for these two effects, a unified and quantitatively accurate description of the complete amplitude evolution for both the double- and triple-shocked interfaces is achieved. The present study reveals that the mechanisms governing the second reshock are closely analogous to those governing the first, offering new insight into the instability induced by multiple reshocks, which represents one of the hydrodynamic mechanisms contributing to implosion instability in inertial confinement fusion.</p>