The sound of any non linear effect, e.g. a saturating device, is affected by the shape of the spectrum of the incoming signal.
A classic trick is to boost or cut a frequency range before the saturation happens and then applying the opposite equalization to the output.
(click to enlarge)
A nice use of this is to cut some low range before the saturation happens and to restore it on the output. Low range gets less saturated and keeps its dynamics and richness while mid/high ranges are saturated giving more edge and air.
You can do it with two instances of a simple equalizer (the simpler and cleaner, the better). This trick gets really interesting when the emphasis is dynamic, though, related to input level and with its own timing.
A tool that can do it is Fooler.
Try this:
- Low frequency: 100 Hz, -3 dB.
- Mid frequency: 1.5 kHz, +2 dB.
- High frequency: 5 kHz, -6dB.
- Mode: 7.
- Set the track to a short repeating loop and experiment with Threshold.