In this paper, we present an experimental study of gregarious fish collective behavior in the presence or absence of biomimetic vehicles. This study is aimed at developing a first understanding of fish shoal controllability using robotic exogenous mates. Macroscopic features of the group schooling are identified through laboratory experiments, conducted in a controlled environment. Experimental evidence proves the existence of qualitatively different shoal collective responses to the exogenous mate. We adapt global observables from statistical mechanics to capture the main features of the shoal collective motion, and identify possible distinct states of aggregation. Further, we investigate the effect of the exogenous mate on the shoal by using a diffusion mapping analysis performed on the global observables. The analysis shows that the exogenous mate is able to exert organizing control actions on the schooling behavior that generally result into a higher cohesion for the shoal.