Your 6632A is doing fine, according to its specifications, there's nothing to be repaired, and nothing to be fixed or made more 'accurate'.
Explanation: These PSUs have a 12 bit DAC for setting the output voltage, at 20V max. output, that is about 5mV resolution of the output voltage, exactly the granularity you already recognized. The accuracy of this ouput is specified as 10mV, so you're already below the accuracy specification.
See specification parameters 'programming resolution' and 'programming accuracy', or alike.
The actual output is read back by a separate A/D converter, for the A model, originally it was also a 12bit one with 5mV resolution.
The later 6632B has even a 16bit ADC, the 'DC measurement accuracy' is 3mV and its resolution is a bit more than 1mV (I think).
The discrepancy simply arises from the different DAC vs. ADC used, i.e. at which point the respective bits flip over.
In the end, it's just a precise PSU (within the specification limits and DAC / ADC limitations), but not a kind of voltage standard, so please do not exaggerate the comparison with your 5 1/2 digit DMM.
Instead round the digits appropriately, i.e. to about 5 mV.
Frank