"Digital display" is not the point. I have antique needle-meters with antique calibration stickers.
"Calibrate" to what accuracy? What are you measuring?
For most of my work, I stick it on a 1.5V battery and I stick it in the wall. A fresh carbon battery reads 1.56V. I usually know my wall voltage from several meters and also lamp life/brightness, and if a meter reads close to expected that's good enough for anything I do.
"Continuity" is for trailer lamps. If it beeps when shorted, that's something. There's always a go/no-go threshold, often 100 ohms.... but even in trailer-lamps a 99 ohm "beep" is not good enough to light the lights. So when it really matters you go over to an Ohms range, and check that against a box of cheap resistors (they are all 5% now except when they are 2%).
FWIW, I have un-trimmable meters 30 years old which still read within 2% of what I think they should. Mostly they work "right", they work "odd" because the battery is weak, or they work "way wrong" because something inside is sick.
Yes, meters can drift, and old needle-meters weaken with age. My 1981 MM now reads 12.3V on what I think is a 12.6V car battery. I know that and accept it. Mostly I'm looking for 11V (sick battery) or 15V (sick regulator), not part-Volt differences. And my other meters have shown negigible drift.
If you are trimming electronic amplifiers for 0.234V at TP13, then you need to check near that 0.234V point against a better meter which is occasionally compared to an even better standard.
If you want to know if there is near 230V at a motor, sticking the meter into a familiar wall outlet may be sufficient for your company's purpose. If they want you to check for contacts opening and closing, a beep test may be good enough.
They DO need to watch for field-meters which have been dropped, abused with 8,000V, or left out in the rain to corrode. (However I'd want a weekly quick-test, not annual.)
If you must use the boss's tool, then it is the boss's problem, NOT yours.