As others have mentioned, a problem with pulling a second wire through a small tube with existing wire is it may get tangled around the existing wire, or burn the insulation with friction as you pull it in.
If it were me, again, as others have mentioned, I'd tie a clump of cotton or a plastic baggie to a piece of strong fishing line and suck it through the conduit with a vacuum. It should pop through in an instant. Crazy fast. Then use the fishing line to pull in a heavier cord, then the cord to pull the new wire.
If that doesn't work, then there's probably a blockage in the conduit. Next bet is to use the old wire as the pull cable. Cut it off at one end, tie the new wire onto it(run another pull cord with it this time for future use), and pull it through.
Either way you do it, use plenty of pulling lube. It makes a HUGE difference and helps prevent friction burn-through.
And it's cheap!!!
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