IMO, you would be better off getting one TT, one arm, one cart for that kind of money enough compromises for one arm and cart!
I agree with Swampwalker. $2K would barely begin to buy one decent vinyl front end. To hope for that plus a second arm and cartridge isn't realistic. Even if you could find such a setup you'd end up with a poor approximation of both types of sound, especially on the resolving/analytical side. True resolution is hard to do, and it's never cheap.
Get one rig that's as close to analytical/resolving/neutral as monies allow. It's easy to make a resolving rig sound romantic. I can think of a dozen different ways, many of them free. But there's no way to recover the information smothered by an inherently romantic cartridge, arm or table.
P.S. If you must have opposing, artificial colorations instead of musical neutrality, how about one decent $2K rig plus a tube phono stage? You could swap tubes depending on the flavor you want. Finding tubes that change a "tight" sound to "tubby" is neither difficult nor expensive.
I generally agree - your money might be better invested in a single arm and table. If you still like to get two different flavor of cartridges, you could use an extra armwand or headshell if you like:
To give you some complete constructive solutions in your price range:
VPI Scout/JMW9 + extra armwand + 2 cartridges of your choice
Technics SL1200 + extra headshell + 3 cartridges
A few more good arms with exchangable headshells/armswands:
Just a thought....
I will suggest that $2000 can get you a competent enjoyable set-up, but will add my opinion to the others' above that 1 table, 1 arm, 1 cart is the right way to start. A second cart is easy enough to add later just by adding a cart to a headshell or armpipe and this could give you "romantic-on-demand."
If you are willing to go the DIY route, you might try building a plinth for an idler wheel system. From all the raving goin on, it probably give you a very respectable table, and the plinth you build could be used to later accomodate multiple arms if you wanted.
I will answer the actual question that was asked. A really nice setup would be a Micro Seiki DDX-1000 with Grace 714, SAEC WE308, Audiocraft (Ultracraft), Lustre GST801, Micro Seiki MA-202L, etc. Price should be around $1200.00 or less, with a cartridge. Add a second armboard for $300.00 and you have $500.00 for something a bit more modern, perhaps an Ittok or Hadcock. Later, you can still add yet another armboard and arm. Splash out on a Denon 103 for the old school arm.
I have a Technics SP10MKII with SME 3012SeriesII and Audio Technica ATP-12 arrms, and Denon DL-103R and Denon DL-102 (mono) cartridges. All but the cartridges were purchased used, and the total price was $1,350. Of course I had to make my own plinth, but that is what gave me room to have two arms. But then having not heard a "high-end" turntable, maybe I don't know what I'm missing. I do know I'm hearing music, however.
Marty- You may have made a math error (like it did a few days ago. You've used up the whole budget on TT, 2 arms, 2 armboards and 1 cart. I know its pretty close, and you could probably do something with a SOTA for example, 2 different REGA mount arms (need only one armboard) and 2 carts. But the hassle of installing a new arm on the old armboard would be probably more than installing a diff cart on the arm. Maybe that's the way to go, now that I think about it. Get good at swapping carts and go that way for a while, until you can afford a second arm. As for me, I would be VERY careful on a used cart. I've sold one that was in great shape, but there are lots of posts/disputes in the forums about problems with used carts. If you can get one from a very reputable member and get a detailed provenance, then its fine, but otherwise, a real crapshoot,IMO.