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The Wiener--Hopf factorisation of a L\'evy or Markov additive processdescribes the way that it attains new maxima and minima in terms of a pair ofso-called ladder height processes. Vigon's theory of friendship for L\'evyprocesses addresses the inverse problem: when does a process exist which hascertain prescribed ladder height processes? We give a complete answer to thisproblem for Markov additive processes, provide simpler sufficient conditionsfor constructing processes using friendship, and address in part the questionof the uniqueness of the Wiener--Hopf factorisation for Markov additiveprocesses.

Markov additive friendships