You can remove pieces and re-gear, but it costs silver to remove.  

There is no way to store a second set of gear locked to a champion for a "swap".

That would be an awesome feature, and it has been requested before, but I have no idea if it has ever gotten any traction @ Plarium.   

Good news is that something in this vein of gear sets for swaps is coming. :)

When though Q.  Inquiring minds want to know.

It's me.  I'm the inquiring mind.