If multiple phaser weapons are hitting the target - yes.

Each weapon can proc individually (once per activation sequence) and ignores the effects of other weapons, regardless of the source. Meaning that if 3 people are firing 3 phaser weapons each at a single target, that's 9 separate chances to be hit with the Subsystem Offline proc, per activation cycle.

The same mechanics are true of all such weapon procs.

Implementing a short-term immunity if you are the victim of such a weapon proc is not outside the realm of possibility, but I'm not certain that the current functionality is actually problematic considering the low overall proc rate of phaser weapons.