The normal practice I have always used is to use manufacturer's tolerances. If I have a specific type of caliper, regardless of where it is used, I calibrate it to manufacturer's tolerances.
If I have a much tighter application where measurement accuracy must be much better, I would select a more accurate instrument. I may use a lower cost dial caliper for a lower accuracy application. I may use a very good digital caliper for the higher accuracy requirements.
In both cases, I have two different specifications because I have two different instruments, which are designed for two different levels of accuracy.
I recommend not using multiple different tolerances on the same kind of instrument. It can be done, but you need a well documented program to assure you calibrate each one to it's own specification.
But it has a high likelihood of problems. There is always the possibility an incorrect instrument can be used for a measurement, which creates product risk. There is increased likelihood for error when you perform the calibration. If you receive ten calipers, all of the same type into the lab for calibration, and five are to be calibrated at one specification, and the other five, to be calibrated to another specification, there is possibility to erroneously calibrate to the wrong specification.
My bottom line recommendation is to specify a caliper with adequate accuracy for each task, and calibrate each caliper to manufacturer's specifications. This is an unambiguous method. When a caliper is received in the calibration lab for calibration, you observe manufacturer and model, pull the specification and procedure for that manufacturer and model. Then calibrate to that specification. It becomes your acceptance criteria.
If the caliper is not at least 4 to 10 times more accurate than the measurements you are making, it is not adequate for the measurement.
The only way to improve specifications on a specific caliper to something better than the moanufacturer's specifications, is to used some time consuming statistics to prove that it can actually operate better than it's specification. That can be difficult if you don't have the people in your company who know how to do it and have time. It is also difficult to defend in an audit.
I'm not sure if this answers what you need to know. Please let me know if there is more detail you need.