Modern transit systems seem to avoid this type of operation like the plague. They prefer to force riders to transfer, or else fall back on the "odd trains to X, even trains to Y" type of operation, neither of which is ideal... it's a prime example of transit providers optimizing service for their convenience, rather than passengers'.
The San Diego North County Transit District has just announced plans to to schedule a mid-line split in for their new SPRINTER trains. The SPRINTER route is purely linear, but the idea is to improve service in the early morning. The first train of the day will begin at Escondido, the eastern terminal, run westwards to the midpoint of the line and split, with one half continuing west to Oceanside and the other heading back east. This will give the eastern half of the line eastbound (countercommute, I guess) service an hour earlier than was otherwise scheduled.
So if SPRINTER can do it, why not other transit systems?
- On weekends, BART could run combined trains from Millbrae to Oakland, then split them into shorter trais to Richmond, Fremont, and Baypoint.
- CalTrain, if/when it replaces locomotive-hauled trains with EMU's, could replace it's half-local/half-express trains (trains that run local in the north/sound end and express in the other end) with trains that run local half way and then split into a local and express.
- CalTrain, if/when it extends southwards, could split trains to serve Hollister, Salinas, and Monterey.
- Dumbarton Rail, if and when it gets built, should run combined trains across the bridge, and then split them in RWC, one half heading to SF and the other to SJ.
The people who run transit agencies are very good at coming up with reasons why new ideas can't be done, but if SPRINTER sets a precedent for splitting trains, it'll be a little harder for them.