I agree that your internal processes should dictate what to do about late calibrations. And yes, what did happen that they became late?
A robust recall system gives plenty of advance warning, via email and/or distributed hard-copy notices to equipment owners and supervisors, or other responsible persons, that equipment is coming due.
The only reason a grace period is needed is failure of the above; a grace period is an excuse for non-compliance.
Upper management buy-in is necessary to enforce metrology system policies. They are the hammer.
Extensions should be granted before, not after, they go overdue in accordance with your policy (30 days is the max at my location), which should include historical evidence that the equipment will have a high probability to stay in tolerance.
Extending equipment by longer is effectively changing the recall interval. Since probabilities are part of establishing the interval, including end-of-period reliability at either the model or test point level, you diminish their robustness when the established recall period is extended by too long (tail wags dog).
I would liken checking a reference artifact (gage block) with a caliper to make a serviceability decision to using a hand-held DMM to determine if a Multifunction Electrical Calibrator is OK. Not a desirable method.