heavy cavalry engaging heavy cavalry

[Sean Manning]

On the original topic, the tilt, or fence along which both horses ran, was invented for jousts because horses often crashed into each other. See Anglo, Martial Arts of Renaissance Europe, p. 227

Maurice said that lancers should close closely together and charge as a solid mass (Strategikon 3.5). I'd argue that his implicit target is other cavalry. This fits with my readings in later medieval sources

Edit: A famous classical case is the fight between Alexander's Thessalian lancers and Darius' Bactrian cataphracts at Issos. Rufus tells us that the Thessalians were driven back and ridden down as long as they were face-to-face with the Bactrians, but charged in when the Bactrians turned and exposed their flanks. The cavalry on both sides wore armour, rode in close order, and were armed with lances so they are "heavy" by any definition.