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LP8555: I2C Bus Sharing With LP8557

Part Number: LP8555
Other Parts Discussed in Thread: LP8557,

The Configuration of the Device we are designing contain 4 separate LED Drivers (LP8555*3, LP8557*1 all from TI).  We need to Control all 4 LED Drivers from the same Control Chip through I2C interface.  However, the Control Chip only has 3 I2C buses available.  Therefore, we are evaluating the feasibility of the design that one of the LP8555 driver share the same I2C bus with the LP8557.(Shown in the diagram below)

Is there anyway for the Control IC to identify each of the 2 ICs (LP8555 and LP8557) that are tied to the same I2C bus, and communicate with each of them independently?