(a)
The plaintiff and defendant, respectively, may be allowed, on motion, to make a supplemental complaint or answer, alleging facts material to the case occurring after the former complaint or answer.
(b)
The plaintiff and defendant, or petitioner and respondent, may, in any action in which the support of children is an issue, file a supplemental complaint seeking a judgment or order of paternity or support for a child of the mother and father of the child whose paternity and support are already in issue before the court. A supplemental complaint for paternity or child support may be filed without leave of court either before or after final judgment in the underlying action.
(c)
Upon the filing of a supplemental complaint, the court clerk shall issue an amended or supplemental summons pursuant to Section 412.10. Service of the supplemental summons and complaint shall be made in the manner provided for the initial service of a summons by this code.