If the background is predominantly tones (e.g. compressors, fans, mains hum) their influence can be reduced by the synchronous pre-averaging of multiple sweeps. The phase of the background tones will be different for each sweep so when the sweeps are averaged the sweep signal maintains its level, since it is the same every time, but the background is reduced. That also works to reduce the effect of random background noise. The effect isn't huge, about a 3 dB improvement overall for each doubling of the number of sweeps, so around 9 dB for 8 sweeps.
Using longer sweeps also helps, since the longer the sweep the more energy it has compared to the background. There is a similar 3 dB improvement for each doubling of sweep length, longer sweeps can be used with your UMIK as well.