would making the inner delta wire driven be helpful...
It depends what you are trying to accomplish. You can certainly build an antenna
like that, the question really is does it give any improvement in performance. And
to answer that question you have to know what aspects of performance you want
to improve on.
On the band where the loop is full wave resonant, it won't add much. That's
because maximum radiation is broadside to the loop (straight up if the loop
is horizontal) and the reflector isn't in the right place. Not only that, but there
isn't room for a loop of the same size - or larger - to be placed inside the first
one. If you want gain in one direction with such an antenna you would need
to turn it into something like a Moxon (or the forerunner VK2ABQ beam). But
then it isn't a full wave loop, and won't work well on harmonics.
One reason the horizontal full wave loop is popular is because because the
radiation pattern moves more towards the plane of the loop on the harmonics:
for an 80m loop used on 20m or 40m there is a null overhead and more radiation
at the lower angles (useful for DX) than overhead. In fact, the longer loop (2 or
4 wavelengths in this case) will have a better pattern for working DX than a full
wave horizontal loop at the same height. That's why you don't often see
nested loops in the same way you see dipoles, except in multiband quads
where they use a separate set of elements for each band. (There is also the
problem that, if you put a 80m loop and a 40m loop with the feedpoints in
parallel, the 80m loop will take a significant percentage of the power on 40m,
unlike the case with dipoles.)
You still can't add a reflector loop easily, but you could add a series of wire
reflectors tied end-to-end with lengths of rope and bent into a loop inside the
outer one. By choosing how to position these you could probably get a bit of
gain in certain directions at the expense of others. There are a number of
other arrangements, but I don't think any of them will make a big difference.
(Hmmm... maybe if the inner loop had some folded stubs to reduce the
physical length while increasing the electrical length...)
One alternative is to add an identical
loop below or above the first, to get
some broadside gain on those bands where the spacing is 1/2 wavelength or more.
This probably requires more height than many hams can accommodate with their
loops, since generally you don't get worthwhile gain by stacking two antennas
until the lower one is at least half the height of the upper one. (Implying a
minimum height of about 60' to get useful gain on 20m, with the second loop
at half that height.) Both loops would be fed in parallel in that case.
But the first step is to be clear about:
1) is this for operation on just one band or multiple bands?
2) are you concerned with gain in just one direction, or in all directions?
3) what other objectives are you trying to achieve?
You certainly can build such an antenna, the real question is whether there is
any benefit to doing so.