You can transplant big tomato plants. However, I wouldn't recommend it if it's not a tomato that fruits all season until the frost. If it's an early, all-season variety that should help. If you want to do it, here's what I would recommend:

* Pick all the fruit (green and all). You may even want to pick all the blossoms. Although you can leave the fruit on, it may set the plant back in its development. Fruit and flowers that grow after the re-transplant are probably going to work out better than older fruit/blossoms, too.

* Pull up the plant when it's dark or otherwise not sunny (even just several seconds of bright sun can really damage plants with recently damaged roots, as well as cuttings with no roots)—don't bother saving much if any of the soil (it'll have to get used to new soil anyway, and you might not want to transport a whole bunch of soil). If there's a huge root system, feel free to cut the roots off at some point. Any roots at all are better than none.

* If the plant is too big, feel free to prune it down to size (the size probably doesn't matter too much, at this point, anyway; you can use the trimmings for cuttings). Bright sun damages plants with recently damaged roots more the more leaves the plant has. Lots of leaves on a freshly dug up plant in bright sun is pretty much death to a plant.

* Keep the plant away from sun while you're transporting it. Keeping the roots moist and the plant cool during this time may also help (but avoiding bright light shining on the leaves is essential; bright sunlight will cause the plant to wilt, become stunted, and it may not recover; in fact, it may even die quickly). Too much sun (and/or too much nitrogen), too soon, I believe, is the number one reason most transplants that fail fail. Tomatoes only need two or three days reprieve from the sun, while some other kinds of plants need more.

* Soak the roots in water for a couple days. The roots will start to grow again (they grow fast in water when there are already roots to start with; it takes longer to root cuttings, but tomato cuttings aren't extremely difficult to do—I recommend rooting tomato cuttings in soil, and not in water), and because it's been a couple days since the roots have been damaged (and the roots have hopefully healed some), the plant will be less likely to experience transplant shock.

* Then transplant.

* To further reduce the risk of transplant shock, add potassium sulfate to the soil at transplant time (do not add any nitrogen—nitrogen could encourage transplant shock). Do not add a full NPK fertilizer (those have nitrogen—usually a lot—which is not good for transplanting). Potassium helps plants to absorb water; it strengthens them, too, and is supposed to be good for plant roots. I've heard a rumor that phosphorus might be good here, too, but I've only tried potassium sulfate in soil with transplants and cuttings (and it works quite well)—so, I can't speak for the benefits (and/or drawbacks) of phosphorus at this stage of the plant's life. Phosphorus is said to be good for plant roots. If your soil is already high in potassium, don't add more (too much potassium can inhibit growth—but the right amount can encourage it). If your soil has lots of composted bark in it, or such, it probably has plenty of potassium. You can tell if a tomato has a good supply of potassium because the stems are not easy to bend or break (the roots are stronger, too, it seems).

Re-transplanting a tomato can set it back significantly (a month or two), but the plant can still go on to produce more fruit. It just may need time to adjust. If you have a longer season, it shouldn't be anything to worry about.

I would suggest doing both cuttings and the transplant, and see which works out the best. I haven't tried this with a fully mature plant with ripe fruit (but I have transplanted somewhat mature plants). I know people dig up tomatoes to overwinter them in their garage; so, if they can do that, you can do this. Actually, I've overwintered one, too (but not in a garage).

If you can take the whole plant (and all the soil) out without disturbing the roots much, and directly put it in new containers the same size, that would probably be more effective than what I mentioned above (although you still may want to have it avoid bright sun for a day).