  A study of the modifications of the magnetic properties of
Ho$_{2-x}$Y$_x$Sn$_2$O$_7$ upon varying the concentration of diamagnetic
Y$^{3+}$ ions is presented. Magnetization and specific heat measurements show
that the Spin Ice ground-state is only weakly affected by doping for $x\leq
0.3$, even if non-negligible changes in the crystal field at Ho$^{3+}$ occur.
In this low doping range $\mu$SR relaxation measurements evidence a
modification in the low-temperature dynamics with respect to the one observed
in the pure Spin Ice. For $x\to 2$, or at high temperature, the dynamics
involve fluctuations among Ho$^{3+}$ crystal field levels which give rise to a
characteristic peak in $^{119}$Sn nuclear spin-lattice relaxation rate. In this
doping limit also the changes in Ho$^{3+}$ magnetic moment suggest a variation
of the crystal field parameters.
