Slightly off-topic, but the text-book method for changing the "focus" of distortion is the concept of "emphasis".
The trick is simply...
->[EQ]->[Saturation]->[EQ]->
...where the second EQ undoes the first one.
This is an essential concept in tape and vinyl production and playback, as well as broadcast (i.e. broadcast limiters). It's also what you'll find in most guitar/bass amps and tools.
The main reason for the heavy use of emphasis in analogue processors and storage media is that you can basically "shift" most of the distortion out of the circuit bandwidth (and thus audible range). This is done by boosting the highs by several dBs at the input and attenuating the highs by the same amount at the output. But this is also great for dramatic saturation effects. Beware, this is highly problematic in the digital domain, since you'll only force the production of a lot aliasing, - which will definitely be in the audible range.
However, this works quite well with good digital saturators (i.e. those using oversampling or other anti-aliasing techniques). All better sounding ones will have some kind of emphasis included anyway.
This technique also sounds very cool with compressors and especially limiters. It acts similar to a sidechain EQ, but sounds dramatically different. Give it a try!
Another nice thing you can do with this facing EQ structure is to remove the saturator and only use the EQs. This will allow you to precisely distort the phase at a certain frequency without changing its amplitude. Two complimentary filters in series basically form an Allpass filter. That is, everything passes through - except that the phase will distort (i.e. a certain frequency region is more delayed than another). This is a subtle but powerful tool for mastering - but it's also useful during a mix, a very flexible alternative to the phase invert button.
Ok, now I hope I didn't confuse you.