We present a quasi-model-independent search for the physics responsible for electroweak symmetry breaking. We define final states to be studied, and construct a rule that identifies a set of relevant variables for any particular final state. A new algorithm ("Sleuth") searches for regions of excess in those variables and quantifies the significance of any detected excess. After demonstrating the sensitivity of the method, we apply it to the semi-inclusive channel e mu X collected in 108 pb^-1 of ppbar collisions at sqrt(s) = 1.8 TeV at the D0 experiment during 1992-1996 at the Fermilab Tevatron. We find no evidence of new high p_T physics in this sample.