I believe if they are shooting a Cat 3 ILS then they must have at least two.
Now a-days, airliners are more dependent on autopilot than ever. Cat 3 ILS approaches allow aircraft to fly under autopilot very near, or even onto the runway, so it is critical that it works and works properly. Autopilot is also needed to fly with Reduced Vertical Separation Minimums (RVSM) between FL290 and FL410, which allows controllers to space aircraft vertically by 1,000 ft rather than the 2,000 ft required at those altitude before.
The reason for having 3 instead of 2 redundant systems is for voting logic. This is also commonly seen on INSs. If you had 2 INSs and they each came up with a different solution, it can be difficult to tell who's is right and who's is wrong. This usually means that pilot action is required to decide which source is bad. With 3 systems, when one comes up with a different solution than the other two it is much easier to determine that it is bad and to automatically invalidate its solution.