Experimental and theoretical studies have shown that nonmagnetic semiconductor-metal hybrid structures can exhibit a very large magnetoresistanceeffect, the so-called extraordinary magnetoresistance (EMR) effect. The EMR can be useful in magnetic-field sensors and read heads. We show that the sensitivity of a linear hybrid structure can be further enlarged by using an optimized configuration of currentleads and voltage probes. Strikingly, we find that the EMR and the Hall effect cooperate and thereby improve the performance. Our findings also explain the origin of the recently reported sensitivity increase in a nanostructured EMR device obtained via interchanging one lead and one probe [J. Moussa et al., J. Appl. Phys.94, 1110 (2003)].