TPS2121: Run two in parallel to double the current?

I likely will need a little more than the 4 to 5A offered by a TPS2121.  6A should do it. 

Can I put two TPS2121 or TPS2120 in parallel and tie the outputs together?

Note: My two input voltage rails are 5V#1 and 5V#2.

I was thinking that I could share the resistor divider networks for common PR1, OV1, IN2 and OV2 inputs.  That would reduce variations for those functions.

Note sure about the CSS capacitor.  I could probably use separate "identical" resistors for the ILIM.

Also, I could use either a TPS2121 to sense the two voltages or TPS2120 and a select control line, a "PWR GD" from a previous stage 12V-to-5V regulator.

Since the these devices have internal voltage references, any differences in the voltage references and comparators between two devices would show up as slight different transition times on the outputs.
While my two 5V inputs are pretty close in value, they come from two different sources so I'm sure they are not exactly the same and therefore when the outputs are changing from one source to another I could have slightly different 5V outputs tied together for a short time.

I see a previous post "TPS2121: larger continue current solution."

I am a digital designer and FPGA programmer.  My analog skills are decades rusty.

thanks