We don't have synonyms for buddy up yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are buoy up, muddy up and buy up.
(v) :
(informal, intransitive) To form small teams, especially pairs, often to reduce the likelihood of any one person suffering harm without being noticed or to suit the nature of a task to be accomplished
(v) :
(informal, intransitive) To form small teams, especially pairs, often to reduce the likelihood of any one person suffering harm without being noticed or to suit the nature of a task to be accomplished