“Non-exclusive” arbitration clauses provide that disputes “may” be referred to arbitration (rather than “shall” or “should” be so referred). The Privy Council clarified the nature of these clauses in a recent case but uncertainties about their effect still remain.
Ultimately, parties would be well-advised to avoid “non-exclusive” arbitration clauses and opt for exclusive arbitration clauses, if what they really want is for their disputes to be resolved by arbitration. If the parties choose a “non-exclusive” arbitration clause, then they should make sure that they avoid issues by making express provision for the litigation costs in the event of a stay and expressly naming a litigation forum.