480 three phase to 208 three phase

Yup, a transformer. 480 to 240 will be close enough. In the small sizes, used ones seem to show up fairly often. Check with the used machine tool dealers and electrical equipment rental shops (I got my X-mer 240 - 600, 3P from an electrical equipment rental shop, $100).
 
When you speak of transforming from 208 to 480 , the question arises "what are you driving?" If it is just a motor, or are there a large number of relays involved?

The quick and dirty solution is just to use a transformer (two single phase) in "open delta" configuration to go from 240 to 480 volts. Most equipment that is rated 240 will operate on 208, perhaps with a little heating. If there is too much heating, using a "boost" transformer configuration can bring it to exact voltage. I offer some insight into that problem, in single phase, in http://www.hudsontelcom.com/uploads/ShopElex.pdf This calculation involves a slightly higher current as well that should be allowed for. There are many other configurations for such a transformer, it really depends on what you can lay your hands on and how much time and money you are willing to invest.

If there is just a matter of a motor and starter, and if the motor is a dual voltage device, rewiring the motor and changing out the contactor is a much "cheaper" conversion, provided you do your own work. Basicly investing time vs money, your choice. If there is a number of voltage sensitive devices such as relays or internal (control) transformers, transforming the incomming line might well be the best option. There are transformers that make this specific conversion, but make sure the wallet is prepared for such a purchase. Sometimes this is done with taps on such a transformer known as a dual purpose device.

There are many such vendors such as described above. Finding one locally is preferred as such a transformer will be quite heavy. Read as shipping cost as expensive as the transformer itself. Further, the transformer will be mostly copper windings around an iron core. They are never cheap inexpensive for that reason alone. A twin coil starter(reversible) is a much better bargain, if it will solve the problem.

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I was thinking of HGR also, but a bit of a drive for you
 
I'm no expert, in my shop I have 480 Delta to 208Y transformer which runs my entire shop. (not all 480 is delta) It's rated at 75kva (about 200 amps 208Y) which is big enough that I never worry about overloading it. The downside is that it's wasting about 900 watts continuous as heat and is noisy. I've considered getting a second, smaller transformer for "vacation" loads but haven't acted on it. Transformers are often found used on Craigslist etc for a couple hundred bucks. There's a 45kva 480 to 208Y on facebook marketplace in Pittsburgh for $200 right now as an example. There are several advantages of this setup such as having 110 voltage which is also sometimes useful:), 208 3 phase and using 2 legs, it runs most 240 devices (many motor plates list 208/230). I did buy a buck-boost on amazon for $110 to run my Tormach.
 
This ad just showed up on the local Craigslist. Not cheap ... $1200 and $1500, but a lot less than new prices. Shipping will be an issue, of course!
 
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