My mix mindset generally goes in one of two directions: change everything, or do as the B.E. is doing with personal touches/ improvements if required.
I have the misfortune of mixing on underpowered Guitar Center rigs staffed by novices more often than not, so the first thing I do is fix whatever gain staging issues are present (for example I'm playing in a show tonight and I'm going to have to show up early to fix everything that was wrong at the same place last night, such as making sure they know the difference between line and pickup switch positions on an active DI) and ring out the wedges and room. Next I fix mic placement, patching and so on. Essentially I have to start from ground up and make the show work on the rig they have.
The second philosophy kicks in when I'm mixing on a properly configured rig (I know it's properly configured because either I set it up, or I know the system tech or house guy). This is quite a luxury, unfortunately, but it's very relieving to have a rig with good gbf, headroom, and sound quality. In this position I'll be able to do my own thing within the guidelines of the band's needs, ie: if they have to have it stereo, it will be stereo.
If mid-show I am handed the reigns of the first system, I'll refuse. If I'm handed the reigns of the second system, I'll take them gladly and avoid radical changes, unless something was really bugging me before I stepped in. In that case I'll fix it.