Mr Trim, I'm not sure as to your reasoning behind there being a limit to the number of items that can be unserviceable. Absent the rare case where items are interdependant, the number of items is irrelevant. If it's safe to fly with it broken then it doesn't matter what else is broken (as I said, there ARE exceptions to this, but in general it holds).
As for how many is the norm, I would suggest this varies from airline to airline, and from season to season. Heavier scheduled times of year will inevitably result in less time on the ground to allow for repairs to non safety critical components, and obviously part availability is another big concern.