The HP3458 (8 digits) meters uses a similar procedure and the same 10 V and 10 K starting point for an adjustment.
The Datron 1281 DMM also uses a similar method, though also including a factory calibration for a special ratio transformer, that is usually very stable over time.
Some of the Fluke calibrators use a similar method, though sometimes starting with 2 resistors.
The analysis of the Advantest meter showed that there still seem to be extra correction factors per range involved from a more classic calibration of the ranges, maybe as a seprate factory calibration.
For a reliable calibration one may still need to check the ranges individually, so make shure the transfer between the ranges actually worked as planed
It is more that the calibration constants / adjustment are based on the 2 measurements. The check part of the calibration is usually still done for all ranges.
To make the method of measuring in multiple ranges work well, it needs rather good linearity and thus a relatively good (linear) ADC. The question is of the ADC is more accurate than the resistor setting the gains are stable.
Some meters do a check in different ranges (e.g. part of the self test), but still call for individual adjustment of the ranges.
Some (e.g. the sigilent meter from the last post) even separate for the positive and negative side. The individual adjustment may compensate for some errors (e.g. INL error) and this way give a better result, at least for the shorter time frame.
The method of adjusting to just 2 measurements is in principle not limited to high end meters, and in some aspects it would also make sense (for longer cal. intervals) for the lower end range for a meter.
However so far I know of no lower grade meter to work this way.
Using external reference and the DMM to measure the ratio is possible, but of limited accuracy and a bit time consuming. The internal process has some advantages, though also a few limitations. One would still need a good (low noise) external source, like a calibrator.