Vancouver has one of the best mass transit systems in the world, but I do not miss the crowded trains that happen during peak times. I propose special ‘Overflow’ train cars that sit at the front and back of a train, increasing passenger capacity. This creates a longer train that extends beyond the length of existing platforms.
These Overflow cars have no exterior doors, so they cannot be accessed directly from train platforms. Passengers would board the train normally, then have the option to move to an Overflow car at either end of the train.
Thanks to the on-board alert system, passengers are notified of upcoming stops by digital signage and a voice over the intercom. This ensures passengers who are sitting in an Overflow car can make their way to an adjoining train before their stop. I would also add some sequential lights to point the way to the exit:
I would recommend just one Overflow car at both ends of a train, any more than that and it would be a bit of a trek when boarding or exiting a train. If additional Overflow cars are needed, I would designate them for passengers going to the very end of the line, which has a longer stop time.
Because of their increased capacity, trains with Overflow cars will allow faster passenger movement when exiting or entering the train. This could result in shorter stops at stations, and shorter commute times overall.
As for the safety of an Overflow car, there would be an emergency exit at the front of the car, along with eject-able glass panes throughout.
Dave's Geeky Ideas 
Love the idea. How would you solve the issue where trains still have drivers (such as here in Australia). Our trains have separate entrances for drivers at the front for security reasons. Also having drivers move through crowded trains to get to the cab is impractical.
The separate entrance thing is new to me! I would say they could do a quick pit-stop at a station where only the very front of the train can access the platform, allowing the driver changeover to happen, after which the rest of the train is moved up to the platform for passengers.
But I would arrange it so driver changes happen at the end of the line or at a few designated stops, and that may require lengthening those particular platforms. This end-of-line rule would also be ideal for trains with interior driver doors as well, because end-of-line stops are longer and the train empties, so drivers (hopefully) wouldn’t have to wade through passengers.
Hopefully ‘Overflow’ trains can combat overstuffed trains and crowded platforms, an idea which I confess only had passengers in mind, so apologies for not thinking about drivers.