Er2Ti2O7 constitutes an experimental realization of the easy-plane pyrochlore AFM and orders at 1.1 K into the theoretically predicted spin structure. However, the system appear to be close to a quantum critical point and the ordered state is far from being conventional. Thus, below TN, our original muSR results showed unsually strong electronic fluctuations down to 20 mK that cannot be associated with standard magnon dynamics. This proposal is a continuation of our current study of the effect of dilution of the rare earth (i.e Er2-xYxTi2O7) on the nature and stability of the ordered state. Previously we have seen that long-range order is destroyed for x = 2.5 %, much lower than the percolation threshold for the pyrochlore lattice.Here we intend to measure new compositions of the series with x < 2.5 % in order to study how and why the ordered magnetic phase is destroyed.