Is it possible to run PB137 in parallel to get more charging current?

This video implies it won't work.

 

It is possible but probably not a good idea. Unless the two are very carfully matched and low value series resistors are placed between each regulator's output and the battery the two would not share the load current equally.

You can buy monolithic analog regulators with much higher maximum current than 1.5 amps, and if your intended use is to charge batteries a switching regulator might be an even better choice as it would dissipate less power than an analog regulator. And the maximum current could be higher.

 

Did you have added small-signal Si diode in the PB137 ground lead, cathode to ground lead? If yes than what is your final battery float voltage?