Since the invention of the sustain pedal, a pianist can freely move up and down the keys with all kinds of broken chords. Book 10 of Franz Liszt's Technische Studien (1868-73) includes a large collection of broken chords, usually with both hands moving simultaneously as shown in following example.
In April 1923, The Etude Music Magazine published under the title New Lights on the Art of the Piano an interview with pianist-composer Sergei Rachmaninov. This exercise is written down according to the instructions Rachmaninov gave in this interview.
Anton Reicha (1770-1836) provides in his Etudes ou Exercises pour le Piano-Forté (1803) an interesting exercise in a stepwise chord progression.
Other interesting piano methods with series of exercises are listed below. More can be found on the platform publications.
Hélène de Montgeroult (1764-1836)
Cours complet pour l'enseignement du forte piano, (vol.1) (composed 1788-1812)
Ignaz Moscheles (1794-1870) & François-Jospeh Fétis (1784-1871)
Méthode des méthodes, Op.98 (1837)