On pot calibrated DMMs, you can work on any range that is off, but I luckily have not had to do so on my Flukes.
I don't have an 87III but I do have an 85III and and 85I. For this series DMMs I prefer the older I and III series because of the pot adjusts and I have full service manuals. On the 87V, its impossible without a proper calibrator because it requires specific calibrator references, in a strict sequence, that is all or none [ yes, I have an 87V too].
However, one advantage of the Agilent DMMs: I adjusted a slightly off Agilent 1252a and 1272a because it does allow adjustment of any single or set of ranges, and will accept any reference value, yet its all digital.