I know your question presupposes an Amtrak context, but you may find the pre-Amtrak to be rather interesting as well. The original pre-Amtrak Texas Eagle was a complicated operation.
One of the highlights of the operation was a through sleeper than ran from St. Louis, to, get this, Mexico City. Yep that is right! It was transferred from the Texas Eagle to the Aztec Eagle(National Railways of Mexico) at New Laredo.
In the top years(late 40's to mid 60's) there were two trains:
1.The West Texas Eagle, St. Louis to Dallas, Forth Worth and El Paso. Through Sleepers from New York, Chicago, etc.Much of this train was dropped in Ft. Worth, the part whcih ran on to El Paso was rather short.
2. The South Texas Eagle, from St. Louis, divided I don't remember where, perhaps Palestine, Texas, not sure. But part of it went to Houston and part to San Antonio and Laredo. It was the San Antone section of course, which had the through sleeper to Mexico City.It, too, had through sleepers from New York, perhaps Chicago. Also a slumbercoah from Baltimore to San Antonio.
You will note that the Texas Eagle, at that time, was basically a St. Louis operation. Chicago to Texas business was handled partly by other trains which no longer exist.
There were other through car operations besides the above. For one, there was a through sleeper and coach from Memphis to Dallas/Ft. Worth (that I used that several times when my sister lived in Dallas and I lived in Chattanooga) and a through Sleeper from Memphis to Houston.
So, there was a very short Texas Eagle from Memphis to Little Rock, from which the through cars listed above were transferred to the big trains when they came in from St. Louis.
There were several other extensions to it. Like I say, it was complicated.
There was a train called the Louisiana Eagle from New Orleans to Dallas/Forth Worth, which, in later years, after business was getting bad, combined with the Texas Eagle from St.Louis at Longview,TX, to points west.
There was a big Pennsylvania train called the Penn Texas which operated from New York to St. Louis and many, many of its sleepers were through cars being transferred to the Eagle in St. Louis, and to another train or two. The through sleepers from Chicago were operated on the same line we still have today with Amtrak with trains like the Ann Rutledge.
The slumbercoach referred to above was operated on Balitmore & Ohio's National Limited east of St. Louis.
In peak years the two St. Louis sections operated about 30 minutes headway from each other. In later, slimmer years, the South Texas and West Texas sections were combined into one train.
The Texas Eagle was a beautiful two-tone blue streamliner (though some pullmans were Pennsy tuscan red, and the slumbercoach was unpainted stainless steel) built about 1947, I think. It replaced a heaveyweight train called the Sunshine Special (which I am sure was just as complicated).
It was under Amtrak that the train was repositioned as a Chicago to Texas operation. As I say, before that time there were other railroads going from Chicago, with the Eagle just getting a sleeper or two.