Definitely over-driving. I've often found sending a lot less 'hotter' signal, from whatever you got 'plugged in', and using the EQ to cut or boost the areas of the signal, that 'splatter' (clip), and boosting the ones that need fattening up.
Sometimes for good, fat 'clean' sound, send in a nice fat sound INTO the unit, but turn DOWN the input level, and let the fat signal 'Work' to move your 'needles'. If you are more concerned with the audio level dynamics, ie. your piece has a lot of 'dynamic range', you would have to find your happy medium, as not to overdrive.
A compressor would serve you well....using the 'output' level, more than the compression side.
When I was both playing, and engineering, often we could pre-set levels...now, I tend to use a separate engineer...and by the way, a GOOD engineer, is as important, and should NOT be considered 'less', than one of the actual playing musicians!...and compensated equally...whether it's a live gig, or otherwise.

GfS