We investigate the pulsed flashover voltage of dielectric samples at up to 4 bar SF6 in the simultaneous presence of a high current (> 10 kA, ∼ 20 microsecond pulse) volume discharge nearby. The chosen distance, ∼ 7 cm, between surface and volume breakdown is consistent with conditions found in the Sandia-Z-machine type rimfire switch. For a flashover gap distance of 24 mm and a simultaneous excitation within ∼ 5 microseconds, we observe an average reduction in the flashover voltage from 164 kV to 142 kV at 3.7 bar when the volume discharge is turned on. The test setup utilizing a magnetic switching scheme operating at 320 kV and 10 kA is briefly discussed along with the breakdown properties and the spectral characterization of the volume/surface flashover discharge plasma. In general, UV light propagates relatively unattenuated for wavelengths > 160 nm in the high pressure SF6 from the volume discharge to the dielectric surface, setting up conditions which are conducive to photoelectron emission from the dielectric.