Yes, I3C allows for multiple Controllers on the same Bus. However, only one Controller can have control of the Bus (i.e., can possess the Controller Role) at any given time.
An I3C Bus has one Primary Controller that initially configures the Bus and acts as the initial Active
Controller. Optionally, the Bus can also have one or more Secondary Controller Devices; these initially act as Targets, but any one of them can send the Active Controller a Controller Role Request (CRR) to ask to take over the role of Active Controller. Once the Active Controller agrees to a CRR and transfers Bus control (i.e., transfers the Controller Role) to a requesting Secondary Controller Device, the requesting Device then becomes the new Active Controller.
Note: The previous Active Controller (including the Primary Controller) can attempt to regain Bus control by performing this same CRR process. Once the previous Active Controller passes the Controller Role to another Controller-capable Device, it typically acts as a Target (i.e., with limited scope) until it receives the Controller Role again. The terms Active Controller and Secondary Controller reflect the current role of the Device at any given time, not the Device’s initial configuration or capabilities. See the specification at Section 5.1.7 for more details.
If the Active Controller crashes or becomes unresponsive, then other Controller-capable Devices may use the optional Error Type DBR procedure to test the Bus and regain control if necessary. For details, see the specification at Section 188.8.131.52.8.
Note: This question was updated for I3C v1.1.1 and I3C Basic v1.1.1.