I use an 11R for maybe 50% of my gigs into a countryman DI and out to house.. like Singtall mentioned.. I'd go in and adjust the amp master or rig volume and pull that down to give you the headroom that you're seeking.. you can still get the clean breakup.. you could even really tweak that between adjusting the rig output or amp master AND pulling a bit of breakup back in by tweaking the speaker breakup slider.. I haven't encountered this and I will run a Suhr Riot or Exotic BB Plus in front from time to time depending on what I need for the gig/session/set or shoot.
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Kevin Dillard
NGW/Alfred/Warner Bros. artist/author
DiMarzio Endorsing Artist
Morley Endorsing Artist
Nocturne Guitars UK Endorsing Artist