That's why I now play the Scott Walker guitar live, and have my Tiger available for what I have in it. It is, as suggested, pretty much a one-trick pony. It's a good trick ... but that's all it does sonically, and also it's a strong visual statement that says Grateful Dead.
On my Walker, I put the Super 2 coil cut in the middle, a Lollar Imperial humbucker in the bridge, a Duncan Lil '59 humbucker in the neck -- all of them are splittable. I have that wired to a 3-way pickup selector, plus a second switch that Brad Sarno came up with the idea for when I was pestering about what I wanted to accomplish with this guitar. That puts the guitar's pickup switching into three distinct modes:
1) Les Paul mode -- bridge only, bridge + neck, neck only
2) Strat + Weir mode -- bridge + middle, neck + middle and all three single coil (Weir's signature early 80s Cowboy tone)
3) Jerry more -- middle Super 2, split.
I also had Scott put in individual tones and volumes for each pickup so I can set the levels as you would on a Les Paul, and still get the benefit of the master volume control and effects loop. The downside of that setup is it's a slightly lower output overall on the guitar having two volume controls in series, although the unity gain buffer mitigates the tone loss. And it also has Scott's little blaster which is a nice, switchable boost. But you can't get any more versatile than that. I can get a nice in-between Strat quack, a total 80s Weir sound, use the 3-way to switch between clean neck and screaming bridge overdrive a la Jimmy Page ... or flip the switch and be Jerry.