Hmmm... I guess you're right, there would have to be some form of push against the outer train, but what if you applied a constant force to counter this large enough for the trains to maintain a constant velocity? This should in theory be possible, right? (With massive amounts of energy, ofcourse).
And instead of accelerating the last train past c in reference to the earth, say you split this up into two huge (outer) trains, one with 5 and one with 6 trains, moving avay from each other (one with c/10 and the other with -c/10 in reference to earth)...
Then the innermost train would be moving faster than light in reference to the other innermost train, right? Would it still take to much energy to be even theoretically possible?