Dynamic earthquake triggering, the process through which stresses transmitted through the passage of seismic waves can trigger remote faults to fail, has been shown to be fairly common throughout the globe and especially in seismically active areas of high heat flow and geothermal activity. We explore the possibility of dynamic earthquake triggering around the Socorro magma body, a feature within the Rio Grande rift in New Mexico that exhibits high heat flow and heightened seismicity. Because the area fits the environment type in which triggering preferentially occurs, we examine 319 global mainshocks with Mw≥6.0 for the possibility of increased seismicity rates following the passage of the mainshock waves. We examine local event locations and origin times relative to mainshock phase arrivals for patterns distinguishing triggering mainshocks from nontriggering mainshocks. We find a small triggering response during the time period analyzed, unlike following the 2002 Denali fault earthquake (DFE). This small response corresponds to smaller peak dynamic stresses than are found in other triggering studies (<0.01 MPa versus 0.01–1 MPa). The larger response following the DFE is likely because the earthquake itself was large (Mw>7.0), at a regional to small teleseismic distance (<∼40°), and with strong rupture directivity toward New Mexico, and the mainshocks examined in this study do not fit all three conditions.