I'm not a fan of the TubeScreamer for rhythm because it is a little too opaque and too narrowly focussed for my taste but it does very nicely as a solo/lead pedal.
Reason being, it lops off a bit of bottom end to tighten that up and then it pushes mids.
It works particularly well if you keep the gain down below 12 o'clock and raise the volume to compensate.
People sometimes think they need massive amounts of gain for soloing when really they just need more mids and some volume.
For soloing you need two things.
You need to be heard and you need touch sensitivity.
Cranking the gain up reduces touch sensitivity, which is a bad thing IMO.
It's about dynamics.
Good touch sensitivity is essential for great soloing in either blues or straight ahead rock n' roll.
Pushing mids is essential in order to be heard over the rhythm guitar.
If you have a scooped mids sound, it might work well for rhythm but not for soloing.
It will just sound fizzy and weak and thin.
If you want more gain than 12 o'clock on your TS you can try pushing the TS with another OD box, preferrably not another TS.
Set the first OD box to a fairly flat EQ, trying to get the widest frequency distribution and let the TS do the truncating and pushing.
If you choose to go that route, I suggest dropping the TS gain to below 11 o'clock.
If you're into shred music disregard everything I'm saying here as that is a different animal altogether.
For shred you want the opposite of touch sensitivity.
You typically want a highly compressed sound.
