Looks like Registar can deal with both additive and multiplicative terms simultaneously. Unfortunately I have no idea how that was achieved. It can even handle images that are not linear. (It was produced during the film era.) So it may be doing more than simple multiplicative+additive calculations.
In my own data processing for large telescopes, I first subtract the background in all mosaic panels and make the background zero in all panels. This handles the additive term. Then I conduct aperture photometry on stars in the panels, and use the common stars in the overlapping region to adjust the brightness of the panels. This handles the multiplicative term. Unfortunately, this only works on images with primarily point-like objects and with images that are very well flattened. Amateur images are usually not like this, unfortunately.
In my naive imagination, one may try to use the histograms in the overlapping region between two panels, and match both the central locations and the widths of the histograms. The match of the central location is an additive term, and the match of the width is a multiplicative term. For this to work very well, the panels have to be well calibrated and linear. Noise may add to the width of the histogram, and it can confuse this process.
If you don’t mind sharing the method for the current multiplicative and additive adjustments in APP, I may be able to suggest a method or two that can do both simultaneously.
Cheers,
Wei-Hao