If your budget is $500 like I believe I read farther up in the thread, then I would suggest going with a Plus Top Pro model. It will have the Probucker pickups in it, which are way better than the alnico classics that are found in cheaper Epiphones, and the color choices and flame maple veneer are pretty cool too.
You could also look into Agile as a potential option too. They aren't exact Les Paul copies like some brands, but from what I've heard they are very good value and a little cheaper than the PTP.
My advice would be to check out Kijiji and Craigslist in your area over a 3 or 4 week span. Chances are, you will find something fitting the bill for half the price of new. I've bought new plenty of times, but I've also bought used at least as often and have never regretted the experience - one I pick up and play the guitar, I know if it's a good deal or not. Don't be afraid to walk away and keep looking.
I would think that a good compliment to your treble-rich Tele would be something capable of a deep, rich tone. If this is the case, you should avoid LP - type guitars with only a single pup in the bridge position, because these will emphasize treble also. And the Epi 335 Dot will take you into even deeper tone territory than an Epi LP (or any LP type guitar) The Dot weighs less too.
So you really need to go play some Epi LPs (and other single cut guitars) along with semi-hollows like the Dot, because only you can determine what you like. Also, Epi guitars come in a variety of neck thicknesses, so that's another reason you need to try some out.
@Paruwi: I actually thought of the Nighthawk because, while it does provide "Fenderish" sounds, it does also sport two humbuckers...I think it is the bridge between "full-Fender" and "full-Gibson (or Epiphone)".
Oh, and OP, the 339 will give you the best of the two-humbucker guitars. Even though it´s a semi-hollow, it sounds close (to my ears there is no distinction) to solidbodies. And, it will also provide that woodiness quality. If you hadn´t heard about the 339s, they are like the 335 in a smaller (think Les Paul) size. I love mine to pieces.
And when your guitar try-outs venture into semi-hollow land, try some of Ibanez' offerings in this category. A few months back, I bought a used Ibanez Artcore full hollow jazz box, and was surprised at the high-quality build and the playability. Ibanez also makes semi-hollow electric guitars in in the Artcore line-up -- a number of which will be in your price range new.
I doubt I'm going to do too much in that direction at this point. The only ones I have any vibe at all for are the 339 & the Telecaster Thinline. Are any of the Ibanez guitars similar to either of those two (I know utterly nothing about their line. I should correct that, they're a long way away from their cloner days).
Yes, Ibanez does make and sell a semi-hollow similar to the ES 339, as far as it being a small body semi hollow. Sweetwater has the Artcore AS 73 for $399 and the ASR 70 for $449. They seem to have the 73s in a variety of color finishes.
I am not suggesting you BUY one -- only that you try one out before buying anything. The reason is I find my Ibanez Artcore to have a lot better workmanship than a lot guitars in its price range, and a neck that is more playable -- at least for me. And, of course you need to try out the ES 339 too, as what is best for me may well not be best for you. But it might be, so give these Ibanez models a try!
I think you will find the semi-hollow Tele to be very similar to the Tele you own in all respects. So if you are looking for something different the ES 339 or the Ibanez models mentioned above (your choice) are the best in your price range.
Secondly, these gents are experts in the field but hold on tight as what they are going to suggests will just trigger GAS after GAS after GAS. I'd look for used Standard if on tight budget. One thing though, are you near any music shop? Because if yes give LP and semi-hollow a try first, just to compare which you prefer.
I have Epi's and Squiers (and some other stuff); however I just traded my double fat tele deluxe for a '57 Junior and am planning to sell my classic vibe thinline so maybe I'm headed the same direction.
I hope the experts on this board join me in saying "we are experts as to what gives the tone and playability WE like, but have no idea what others like." So, while the OP should try to play every single suggested guitar, he needs to chose what is right for him. Like he may try the Ibanez Artcore I suggested and decide this neck is too thin for him -- and very thin neck is exactly why I like Artcores. He may find the tone too deep and rich -- and that tone is what I want. While I love my Epi 56 GT P 90 LP, I find the neck to be a half-baseball bat, others have found the same model and year guitar's neck to be too thin. And so on.
I think those who ask for advice here usually know responding postings will be based on the responder's experience and opinions -- which may not be the same as the one who asked.