It is possible to just set one side, each brake system is independent, the park brake linkage splits into two cables, each of which traps pressure on it's respective side. If the respective pedal wasn't depressed, no pressure to trap.
A lousy system, really. Prone to getting set 'softly' so that the aircraft starts to roll imperceptibly. Also the position and actuation of the handle (a straight push down on the console releases it) invites inadvertent release. Drop a Jepp binder on the handle and it's off to the races. A friend of mine turned around in his seat to assist the the still standing FO with something with one engine running. In the process he bumped the handle, they went down an embankment and through a fence.