About possible scenario. The most simple is following:
...
Shifting weight to different rope is common operation in rescue and self-rescue.
Hmmmm, this is quite different than the vague
notion I had : here, you load your 2nd rope
from below, and I was trying to think of some
case where this rope was running beside and
needed to support ... from above!
(To assume that you have just enough slack
below, yet a stuck rope to keep the end away,
is getting pretty picky!

In my vague scenario
it would just be so lonnnng 'til the end (thinking
of doing this exchange in caving, near upper
anchors) that one wouldn't care to use the end.)
In your case, you need also to have sufficient
material in the lower end (aka *2nd* rope) in
order to make some attachment structure
--an eyeknot, likely--; and THEN hitch that
rope into position to be effective.
Frankly, I would simply try putting in a
rolling hitchletting the one, away side of the bight used in
tying fall away, having an effective single-strand
(usual) knot until the closing
half-hitch which
would be a bight. The tying becomes cumbersome
with each additional wrap of to-be-tight & fall-away
bight strands.
--dl*
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