Jon I wrote:
I accidentally cut off the 24 pin ATX power supply connector because I
thought I was going to use the power supply for another purpose, but
that turned out not to be the case. I want to reinstall back into the
desktop, but I have a question: since all the red, yellow, orange, and
black wires were going to be combined (for greater current handling in
non-PC use), I am wondering if I could just combine the same color
cutoff wires from the connector with the ones coming from the power
supply? Would sure save a lot of extra soldering. For example, in case
I'm not clear, can I combine all the orange wires from the supply and
all the orange wires from the connector and solder together? Thanks in
advance.

You could do this, but you'll quite a bit of flexibility if you combine
colors into big fat connections covered in heatshrink or tape. Your
connector may not fit in the case as the cables and patches are too stiff
or in the wrong place etc.