Xarax's ... suggests some odd sort of cordage with many tentacles ?!
Yes, in some sense. The 5, 6 or 7 rope strands, placed around a soft core, ( be it a flexible hollow plastic tube or else), can move
transversely and reposition themselves into the cross section of the compound rope : So, if pressed, there can be three of them in contact with a flat surface, for example. However, they should not be allowed to move
longitudinally, and one or more of them slip, while the others stay attached to the surface by friction.
I described only one possible solution for a compound rope, that can be flattened much more in extend, and much more easily, than the normal ropes do. Knots tied with such a rope will hold better, I believe. Another possible solution is a braided hollow rope, also with a soft flexible core, which can be flattened in a similar way.
With a firm cross section, one has smaller contact patches... with compressive rope, the contact patches get planar. The so-called (by me) "reverse groundline hitch" is a common commercial-fisherman's knot that depends on relatively flat (as thoug compressed) cordage, which is even often used in adjacent pairs, thereby exaggerating the width dimension vs. thickness, and getting relatively large contact patches.
From another thread...
That is exactly what a multi-line rope, with the lines arranged around a soft core, could achieve better.
... it has not translated into people abandoning their round rope for flat webbing very often, for example.
True. There are also other considerations in favour of ropes with a stiff circular cross section. Easiness of handling, storing, go through pulleys, etc.. I guess that there would be some compromise to the degree that such a rope will be designed to be flattened, depending upon material, use and specific application.