I have many different students. One and the same piece I might give to several of them, but approach could be different.
For example: there was one composition, based on a Brazilian folk melody arranged for two guitars. First guitar would play melody and second – accompaniment. With one of the students we analyzed the harmony, saw the familiar chords (that we studied before, like Am, E, Dm etc.) and I gave him a task for our next lesson to prepare several options of his own accompaniment based on that harmony.
It is useful to do it with every piece you play. Especially when there are two players, melody and accompaniment. Analyze harmony and create your own accompaniment.
Sometimes it opens new points of view and generates interesting ideas for interpretation.