fragment boolean

A new boolean operation for paths that inputs a set of closed loop paths that overlap, and outputs new closed loop paths for each subset.
Given three overlapping circles (A, B, C, arranged in celtic knot style), outputs 7 new paths for each area of overlap.
A-B-C, B-A-C, C-A-B, (AB)-C, (AC)-B, (BC)-A, (BA)-C, (CA)-B, (CB)-A, ABC

If given 4 circles where any given circle only overlaps two of its neighbors, it outputs 8 subsets (4 areas where 2 of the original circles intersect, 4 areas where the original circles did not overlap with anything).

I don't know how else to describe it, but the same operation is available through Microsoft Visio (Developer Options >Shape Design > Operations > Fragment).

Although the same effect can be achieved in Inkscape by doing duplicates of the shapes, and performing multiple intersections and exclusions, it would be much nicer to have the option to do it in one click and then choose what to do with each path.

(Sorry if this is the wrong place to put a feature request)