What does 'just or necessary' mean in a polygyny application?

It means the court must be satisfied that the proposed marriage has a reasonable cause. Act 303 section 23 gives examples of circumstances such as the wife's infertility, physical infirmity, physical unfitness for conjugal relations, wilful refusal to comply with an order for restitution of conjugal rights, or insanity. This list is not the only possible cause; the judge may accept other reasonable grounds. The court still assesses other conditions such as finances and fairness. Act 303 s.23(4)(a) uses "just or necessary" (before the amendment by Act A1261: "just and necessary"); the wording in state Enactments may differ, so check the table of state laws. See also conditions for polygyny.