I'm not talking about a calibration in which the unit will read within spec only over some reasonable range of inputs under some reasonable range of conditions around the calibration conditions. I'm talking about something like getting a "calibrated" capacitance meter that only displays the correct capacitance precisely 11 seconds after you insert the capacitor because that happens to be when it displayed the correct value for their calibration capacitor. So that is the only moment in time with the displayed value is the correct capacitance while it is wrong at all times before and after that (even though it still displays a "capacitance", it is just wrong).Now, if your question is more of are there other sample periods for which the calibration is valid, then my answer would be it depends on if the system scales linearly. If so, one could use a different sample period and apply an appropriate scaling factor. Otherwise, one would require an array of coefficients and select the correct one depending on the the sampled value. The more non-linear the system, the more that the calibration becomes an approximation, assuming a constant number of coefficients.

Ok, now my brain hurts.