Another vote for less pre, higher master volume settings. Generally pushing the preamp gives you a real fizzy, buzzy tone but a balance between the two is always a good starting point.
If it's "that" tone then it generally requires the output tubes being pushed to the point that they're starting to overload. How loud that is depends on a bajillion variables. Single-ended, low powered amps will break up earlier and thus at lower volumes, but you won't get a 4x12 moving much air if that's your bag.
A higher powered amp will sound pretty different when breaking up, not least because higher powered amps need different tubes to handle the increased power. Generally you'll also be able to start pushing speakers at these sorts of volumes, and increasing the level of reflections from the room.
One of my favourite amps to record was my Orange Tiny Terror, just because it sounded huge at bearable volumes. My Mesa on the other hand takes my head off, but sounds fantastic when you find the sweet spot.
I like a 57 on axis and a 421 45 degrees off. I read about it in an interview with Joe Baressi and I just find that it nearly always works. An m201 on the cone works nicely, as does an m88 or an RE20 to the side for low end grunt. For pretty stuff I like a 414 and an R122 both on axis, about 6-12 inches away, play with the phase till it sounds about right.
P.S. Trying to push a Twin Reverb to breakup is a bad idea...unless you're in space...and even then it would melt the sun.