Cross sections resulting from scattering that proceeds via an intermediate resonance are shown to be exceptionally controllable using a coherent superposition of only two initial states. Full quantum computations on F+HD(v=0;j=0,1)-->H+DF, D+HF, which exhibits a resonance in one of the reactive channels, support the formal arguments, showing that control is indeed vast. In this case the ratio of reactive integral cross sections can be altered by a factor of 62 (compared to a noncoherent factor of only 3.3), while the ratio of reactive differential cross sections can be altered by a factor of over 6000 (compared to a noncoherent factor of less than 7). These results constitute the first prediction of extensive quantum control in a collisional process.