  Mo$_3$Sb$_7$ single crystals lightly doped with Cr, Ru, or Te are studied in
order to explore the interplay between superconductivity, magnetism, and the
cubic-tetragonal structural transition. The structural transition at 53\,K is
extremely sensitive to Ru or Te substitution which introduce additional
electrons, but robust against Cr substitution. No sign of a structure
transition was observed in superconducting Mo$_{2.91}$Ru$_{0.09}$Sb$_7$ and
Mo$_3$Sb$_{6.975}$Te$_{0.025}$. In contrast, 3at\% Cr doping only slightly
suppresses the structural transition to 48\,K while leaving no trace of
superconductivity above 1.8\,K. Analysis of magnetic properties suggests that
the interdimer interaction in Mo$_3$Sb$_7$ is near a critical value and
essential for the structural transition. All dopants suppress the
superconductivity of Mo$_3$Sb$_7$. The tetragonal structure is not necessary
for superconductivity.
