By rheologically examining poly(vinyl alcohol)-water-Laponite multicomponent suspensions, we report evidence of concentration of adsorbing polymer strictly regulating the aging dynamics in multicomponent Laponite suspensions. The study is performed in the dilute polymer concentration regime. We analyze the observed aging pattern by fixing the non-monotonic transitions observed between temporally achieved suspension elastic moduli and polymer concentration, as the border of a sub-regime. This divides the aging pattern into three sub-regimes, across which the suspension elastic modulus shows an oscillatory relationship with polymer concentration. We also observe that suspensions belonging to first two sub-regimes remained colloidally stable during the timescale of measurement. In the third sub-regime, macrophase separation occurred, while suspensions were aging. For an explanation to this observation, we conducted three complementary measurements on select suspensions from each sub-regime, after they attained structurally arrested state. They are (a) small-angle neutron scattering, (b) structure recovery upon shear melting, and (c) zeta potential estimation. The collective evidences are analyzed to reach a possible explanation. The observation and analysis highlight the effect of concentration of adsorbing polymer on aging clay suspensions and have direct applications in stabilization, rheology modification, as well as polymer nanocomposite preparation.