Cal. Code of Civil Procedure § 1281.3

A party to an arbitration agreement may petition the court to consolidate separate arbitration proceedings, and the court may order consolidation of separate arbitration proceedings when: (1) Separate arbitration agreements or proceedings exist between the same parties; or one party is a party to a separate arbitration agreement or proceeding with a third party; and (2) The disputes arise from the same transactions or series of related transactions; and (3) There is common issue or issues of law or fact creating the possibility of conflicting rulings by more than one arbitrator or panel of arbitrators. If all of the applicable arbitration agreements name the same arbitrator, arbitration panel, or arbitration tribunal, the court, if it orders consolidation, shall order all matters to be heard before the arbitrator, panel, or tribunal agreed to by the parties. If the applicable arbitration agreements name separate arbitrators, panels, or tribunals, the court, if it orders consolidation, shall, in the absence of an agreed method of selection by all parties to the consolidated arbitration, appoint an arbitrator in accord with the procedures set forth in Section 1281.6. In the event that the arbitration agreements in consolidated proceedings contain inconsistent provisions, the court shall resolve such conflicts and determine the rights and duties of the various parties to achieve substantial justice under all the circumstances. The court may exercise its discretion under this section to deny consolidation of separate arbitration proceedings or to consolidate separate arbitration proceedings only as to certain issues, leaving other issues to be resolved in separate proceedings. This section shall not be applicable to an agreement to arbitrate disputes as to the professional negligence of a health care provider made pursuant to Section 1295.