If you buy the 4 strand wire each being about 20 ga and twist 2 of them together per side to make two wires from the four and hook them up, it will work fine.
It would work about the same as if you bought 2 wires of the same kind of wire that is 17 ga.
There will be some differences albeit you might not hear them. Depending on how you twisted them together you might get better RFI/EMI rejection with the 4, you might get more (or less) inductance, and you might get less skin effect (with 4 smaller diameter wires vs 2 bigger diameter ones).
My guess is that you would not notice any difference in the music coming from your speakers. The previous sentence was based upon an assumed level of equipment, based solely on your questions.
There are people with good enough gear and ears on this website that might be able to notice though, and that's why I pointed it out.
Just as an aside, you could buy any thickness and the 4 strands, say each being 16 ga, and make 2 strands from them. They would probably sound similar to a 13 ga wire made from just 2 wires.
In fact, there are speaker cable receipes from coathangers to cat 5 cable. So most all wires have been tried. Some with better results than others.
If you bought a premade wire like DH Labs Q10, and had a choice of terminating them with 4 ends per speaker wire for bi-wiring, or 2 for standard, there would not likely be any difference in RFI/EMI rejection, inductance, or skin effect.
If you bought DH Labs SilverSonic T-14 and made your own 4 strand wire from 2 double strands there would.
Just out of curiosity, wht speakers do you have, and how many sets of binding posts do they have? Is there a brass plate or wire connecting the sets if there are more than one?