For this hobby you will mostly need an imagination and to be a bit of a guitar nerd...
Take any, one classic guitar type and tell us how you would redesign it, what you would change if you were to have the chance.
I'll start with this one:
A Les Paul. I'll start with the Studio model, because unbound neck. Stretch that neck up to a Fender scale length. Make it a through neck that sits parallel to the body (rather than the angled, glued-in neck). string-thru bridge as on the Cabronita Tele. P90 bridge, Gretsch Filtertron in the neck. Pots wired V,V, MV & MT. No pick-up switch on the upper bout; two mini-toggles for independent p'up on/off down by the pots (where the selector would be on an SG). No body binding. Blue metal-flake pain body all over. Mahogany body, flat top, maple neck, pao ferro board.
Don't know if that really makes it an LP any more, but that's the ide here (think: a brand like Fano and how it reinterprets elements of classic design).
What would you do?