Schools prefer recommendations from bosses, unless they state otherwise (for example, Stanford sometimes requires one recommendation from a peer).
Schools prefer recommendations from a "direct supervisor". However, they also like recommendations from senior people:
– Ideally, the recommender will say: "I supervised his work".
– If a senior person that was not the direct boss can say something like "I supervised his work directly and indirectly and we worked intensively together during these X years" it may be better to take that person because he is more senior than the direct supervisor.
– A recommendation from a very senior person that also says something like this can work too: "Joe worked for a few different managers, I am here representing my own experience with him as well as the aggregate evaluation of our organization based on feedback that I collected from most managers who supervised him, data that I collected from his personal file and past performance evaluations".
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