  We have successfully synthesized four Mo$_3$O$_8$-type cluster Mott
insulators (CMI) by intercalating lithium into nonmagnetic precursors to
regulate the Mo$_3$ cluster valence. The resulting materials are
Li$_{1+x}$$R$Mo$_3$O$_8$ ($R$ = Sc, Y, Lu) and Li$_x$Zn$_2$Mo$_3$O$_8$. Our
magnetic susceptibility measurements revealed that these materials display
characteristics akin to a valence bond glass state and suggest the presence of
short-range ordering when the Mo$_3$ cluster valence approximates its ideal
value. These findings challenge the prevailing belief that the plaquette charge
ordering state is an inherent feature of Mo$_3$O$_8$-type CMI. Instead, they
underscore the importance of Mo$_3$ cluster valence in determining the physical
properties of these systems. These insights furnish a fresh understanding of
the Mo$_3$O$_8$-type CMI and open new research opportunities in highly
frustrated magnetism.
