The phrase "branch off" means to create a separate group or division from a main unit. Some possible synonyms for this expression include "split off," "separate," "diverge," "deviate," "fork," "divert," and "part ways." Each of these words carries a slightly different connotation that can be used to convey a particular sense of separation or differentiation. For example, "split off" suggests a sudden and forceful break, while "deviate" implies a more gradual and deliberate shift. "Fork" suggests a branching into two distinct directions, while "divert" suggests a more temporary and minor separation. Ultimately, the choice of synonym will depend on the context in which the phrase is being used and the desired effect on the reader.