Voltage Regulator: how to compensate for voltage drop in cable?
Modifying any cable isn't usually contingent on the number of cores it already has - the modification would need to increase the cores from 4 to possibly 5 or 6 (at the risk of upsetting the balanced data on two of the existing 4 cores).

Assuming you can adequately modify the cable you'll need what is known as "sense" feedback. I'm sure there are chips that can help with this and work with the 0V connection too.

For a regulator that is of the adjustable type there is usually a feedback pin that is able to be used for "sense" type applications but, in probably all the common chips, this would not work effectively because the feedback system may end up oscillating thus, you need an adjustable regulator that can cope (harder to find) or you inject, to the feedback pin, a "slugged" signal that won't upset the chip's usually very fast response time to transient loads.

This can be done with an op-amp that monitors the end points of the cable and, in turn, fractionally and carefully, raises or lowers the feedback pin without upsetting the usually fragile control system that exists within the chip.

Do-able but maybe a little tricky.