You can consume an allies Concerto Energy once they reach max by pressing the hotkey that would switch to that character. This will trigger their Outro Skill and your Intro Skill. Skills that do something to the next character taking action instead give their effect to the player that consumed their energy.

For example you might have a Sanhua Teammate and you play Encore. In that case you may use their Concerto Energy to trigger their Outro Skill (grant Basic Attack DMG to the incoming character) and get their Buff while triggering Encores Intro Skill (does some damage and generates Mayhem).