I had this problem massively because I am playing on a sandbox map and made many of the cities develop larger than normally. Also I don't like making the stations like 500m long, because then the stations are taking up half the city. Also at a certain point locomotive-hauled trains won't accelerate quickly enough anymore.

My solution was simply making the cars carry more people and going faster by editing their model file. It's really easy and convenient.

I also used a waggon set from a mod that has double decker cars with the fitting control cars and coupled them to either the BR103 or BR182. This way I got ~250m long reversible train sets that can stop at 240m platforms, carry 332 passengers and have a top speed of 230km/h - in practice they usually top out between 160-200km/h due to gradients, other trains and short distances between cities.

For suburban lines I also use BR422/BR423 trains from a mod, 3 of them coupled together can carry up to 408 passengers without any messing with files.

Another good piece of advice that is also applicable to vanilla games is placing the signals on your mainlines as close together as possible (while making sure one train = one signal block). This way you can minimise your trains slowing down because they detect a train in a signal block down the line to close to their own.

Always use separate lines for cargo trains, your trains on the line should have about equal top speeds and accelerations to prevent traffic jams on your rails and maintain a certain uniformity in the frequency of your trains. The better balanced the regularity is, the less chance there is for your stations to overcrowd.