Double-decker trains. They're fairly common in North America and continental Europe, where they allow increased passenger numbers for the same length of train, but they have never been adopted in the UK because of our restrictive loading gauge. Britain was one of the first places in the world to build railways, which unfortunately means a lot of our infrastructure (bridges, tunnels, etc) was built at a time when railway carriages were smaller. Now overcrowding is common, and Britsh railways need to accommodate more people. Longer trains have been introduced, but there comes a point where you just can't add any more carriages. The only way to expand is upwards!
Double-deck tramcars were used all over the UK for many years, but adding a top deck never happened on the railways. The Southern region of British Railways experimented with a "double-decker" EMU designed by Oliver Bulleid, which instead of being a true double-decker (as a bus or tramcar), it has dovetailed compartments that resembled a mezzanine more than an extra level.
Now one designer may have come up with a solution. Andreas Vogler's Aeroliner 3000 design has the end vestibules (over the bogies) at platform height, but the centre of the carriage is split into two decks, with the floor of the bottom deck below platform level allowing space for a top deck above. The design is similar, but more compact than the Dutch class DD IR-M double-deck EMUs (pictured).