The generation of spatial rogue waves, or “hot spots,” is demonstrated experimentally in the passively Q-switched Nd:YAG laser system operating in a low-power regime well below the self-focusing limit. Here, we report the dependence of rogue wave statistics on the number of transverse modes that interact in the laser cavity. Our observations show that spatial rogue waves are most likely to occur when the laser exhibits complex output beam configurations that are formed by a large number of interacting high-order transverse modes. These results confirm the hypothesis that one of the main factors affecting the emergence of spatial rogue waves in solid-state lasers is the number of laser transverse modes.