There are shops/yards of varying sizes at New York City (Sunnyside), Miami (Hialeah), Boston, Chicago, and Los Angeles. I'm not sure on the capabilities of all of them, however.
I found a very interesting brochure:
http://www.amtrak.com/ccurl/533/3/Amtrak-Mechanical-Services-201109.pdf
Amtrak considers itself to have three "major back shops" (its term): one is Beech Grove. The other two are at Bear, Delaware (which does heavy work on Amfleets and Acelas), and shops/yards at Wilmington, DE (which deals with the electric locomotive fleet). Together, Bear and Wilmington have the expertise and equipment to handle practically everything except diesel locomotives and dining cars.
I don't know if Bear or Wilmington could be expanded. Bear is the logical place to expand.
The other 12 shops have much more limited facilities. Boston, New York, DC, Chicago, New Haven, and Seattle are on fairly cramped sites and probably couldn't expand too much. Some of the others might be able to expand quite a lot, including LA.
Most of the shops are very close to Amtrak stations. Notably, Beech Grove is about as far from Indianapolis station (~6 miles) as Bear is from the NEC; but Bear is on a branch line which is probably used more for Amtrak traffic than for freight, so shuttling cars to it is easy. (The cars coming and going from Beech Grove are set out at Indianapolis Union Station on a spare track, for the person who asked.)
Beech Grove has been isolated by the repeated drops in service surrounding it. Although it could get tolerable service if CSX was willing to do the shuttling to and from Chicago, it isn't even well located on the freight network any more; most of the lines north and south out of Indianapolis have been downgraded. (Also, notice the difficulty the Cardinal has finding a good route into Chicago.) With Bear and Wilmington already present and handling most of the NEC fleet, something closer to Chicago would be a lot better. I don't know if there are any redundant railyards in the cheap land on the South Side of Chicago -- or perhaps Gary -- but that would be the logical location (lots of connections to lots of lines, not *too* far to relocate Beech Grove workers, room to expand). The freight yards seem to be expanding in that area so there may not be any available space, though.
Perhaps the thing to do *is* to warn the governor and legislature of Indiana that their failure to fund trains to Indianapolis is threatening the viability of the Beech Grove location. If that gets more trains to Indianapolis, great.
Beech Grove is no longer "as central as possible to minimize overall travel time" -- it's now located so as to maximize overall travel time.
Amtrak's shops are already having a problem with "cars not arriving as scheduled" (due to intensive use of the fleet). Accessing Beech Grove only three days a week on one of the most unreliable Amtrak trains (to Indianapolis, followed by a switcher job to Beech Grove!) can only make this problem worse! It would then generally be faster to get to shops located in *Denver*, because the Zephyr runs daily!