  We report on the effects of introducing magnetic and non-magnetic disorder in
the hyperkagome iridate quantum spin liquid (QSL) candidate Na$_4$Ir$_3$O$_8$
by partially replacing Ir$^{4+}$ ($S = 1/2$) with Ru$^{4+}$ ($S = 1$) or
Ti$^{4+}$ ($S = 0$). Specifically, we synthesized
Na$_4$(Ir$_{1-x}$Ru$_x$)$_3$O$_8 (x = 0.05, 0.10, 0.2, 0.3)$ and
Na$_4$Ir$_{2.7}$Ti$_{0.3}$O$_8$ samples and measured electrical transport, AC
and DC magnetization, and heat capacity down to $T = 1.8$ K. Na$_4$Ir$_3$O$_8$
is associated with a large Weiss temperature $\theta = -650$ K, a broad anomaly
in magnetic heat capacity C$_{mag}$ at T $\approx25$ K, low temperature
power-law heat capacity, and spin glass freezing below $T_f \approx 6$ K. We
track the change in these characteristic features as Ir is partially
substituted by Ru or Ti. We find that for Ru substitution, $\theta$ increases
and stays negative, the anomaly in C$_{mag}$ is suppressed in magnitude and
pushed to lower temperatures, low temperature $C \sim T^\alpha$ with $\alpha$
between $2$ and $3$ and decreasing towards $2$ with increasing $x$, and $T_f$
increases with increase in Ru concentration $x$. For Ti substitution we find
that $\theta$ and T$_f$ become smaller and the anomaly in $C_{mag}$ is
completely suppressed. In addition, introducing non-magnetic Ti leads to the
creation of orphan spins which show up in the low temperature magnetic
susceptibility.
