Section 5(1) of the Admiralty Jurisdiction Regulation Act 105 of 1983 creates three disjunctive (not conjunctive) categories for joinder of parties, including peregrini not otherwise subject to the court's jurisdiction. The word 'or' in the provision must be given its ordinary meaning absent compelling reasons to read it as 'and'. The third category permits joinder where 'any question or issue in the action is substantially the same as a question or issue which has arisen or will arise between the party and the person to be joined and which should be determined in such a manner as to bind that person.' This broad power is intended to avoid multiplicity of actions and conflicting judgments in different jurisdictions. An interlocutory order joining a third party to an application to compel discovery, which itself is interlocutory to the main action, does not dispose of substantial relief and is generally not appealable. The interests of justice test for appealability, while paramount, retains the 'gravitational pull' of the Zweni requirements. Where a joinder order merely facilitates proper adjudication without finally disposing of any relief, and where allowing an appeal would cause delay, fragment proceedings, and serve no purpose toward finality, the appeal should be struck from the roll as the order is not appealable.