Well, d, you
can with certain 'less-than-mass-market' manufacturers.
(Well, maybe not
you, per se, in Finland...)
But nowadays, when you count Squier product, MIM, MIA(sia) and American models, Fender markets about 30-40 varieties of the Stratocaster, and maybe as many Teles, and Gibson, if you consider Epiphone to be like Squier is to Fender, offers LP variations up the wazoo.
That's why when I decided I wanted to get a Tele (again), I went for a
G&L.
To start with, they have about a dozen or so 'standard' 'ASAT' models, they make some short stock production runs, and dealers otherwise can custom order them as either they think they'll sell, or as their customers want them. Going thru my local dealer, I custom ordered it as I wanted it. Picked the neck style from 5 options (profile, shape, f/b width), fingerboard (maple, glossed & tinted...coulda picked no tint or no gloss, coulda had the headstock finished to match the body), opted for no f-hole on a semi-hollow swamp ash vs. alder body, the body finish, natural wood binding on the front edge (vs. plastic on front and/or back), and the pg color/material. It took about 5 weeks to come in (they originally estimated 13), and it cost me less than a Fender Custom Shop model.
Heritage the company started by ex-Gibson factory guys almost 30 years ago with the old original Kalamazoo, Michigan Gibson factory, is another company you can do this with. My (same) local dealer is also a Heritage dealer. You want a 'Les Paul' or 335 as you like it? This is the outfit. And it's more 'old school' Gibson than Gibson. I've had my guy spec out a couple for me in the past, but...well, I'd have to pay as much as (maybe a little more) I would for a stock Gibby and wait 2 months to have one just the way I want it instead of settling for an assembly line model off the shelf at a Guitar Center. Gee...why would I want to do that? If I had $2 or $3 Grand, I would.