Before sending the meter out to calibration / adjustment, I would suggst doing some more testing.
A first point is checking for the input current / bias - this can indirectly cause errors and not als calibration services test this. The test is also relatively simple and does not need special equipment.
Another point is stability of the readings, at least in a few ranges, depending on the stable references on can get. This could be something like a few good resistors and maybe a 7 V reference that is reasonable stable over maybe 1-3 months.
A few points (e.g. resistors) could be checked in 2 ranges to check consistancy.
With an old Keithly 20xx meter one may consider checking the age of the filter capacitors and depending on the age consider an exchange. There are quite a few reports of leaking capacitors doing damage with these meters. At the very least check if they already leak.