I RO into a static tank at home, and have 2 DI vessels in the van. The DI's are before the tank, so I just pump the water from the static tank through the DI's and into the van tank.
The biggest advantage is that if I ever run out of water on a job, I can fill up on site and keep on working. DI after the pump should work too,.. I've never heard that it'd damage the pump.