Calibration is about documenting the history of the meter. Adjusting it is not the same. You want to know the rate of change over years so you can predict it. If it is of 0.01% after one year, and an other 0.01 after two years and that stays like that after 5 years then you can predict what the fault will be at other moments and in some cases you can increase the time between calibrations. If you adjust it you lose that data. But if it is outsite de tolerance, then you adjust it.
The calibrator you use must be much better as the meter and if you want to do it right it must be tracable (the Vref has to get calibrated too)
Accuracy specs are given most times for 24h, 1 month, 3 months and a year. But only for certain conditions like f.i. 25 degrees and 70% rH%
Do not touch the inside of a meter and dfo not expose it longer as neccessay. Dirt, greas from your skin and moisture from your breath can degrade performance (not that that will give much problems for a handheld DMM but for 6,5 and more meters this because important.
A Vref IC alone is not very usable. It must be buffered and have a low output impedance, must be aged enough. Most times you need several Voltages.
Besides this there are things like shielde leads, guarding and sense. But also wireresistance and things like the Seebeck effect caused by different metals and temp differences.
Unless you have a tracable voltage and current source and standard resistors you better leave it like it is or send it to a cal lab.