What makes you think the poultry netting is not going to be enough? Depending on where you live, that may be all you need.
I use 2x4 welded wire, which is not predator proof, but it is predator resistant and has deterred all my daytime predators. I have bird netting for the top, which has been good enough to keep out hawks and eagles. At night I lock my girls up in a Fort Knox coop, so my run does not have to be 100% predator proof with 1/2 inch hardware cloth all the way around (very expensive). For me, the 2X4 welded wire hit the spot of good protection for cost of material. If I had unlimited money, yeah, I'd go with the hardware cloth.
It has already been suggested to just add 2x4 welded wire over your poultry netting. Another option may be to add another layer of poultry wire, staggered half way, over your existing wire. It might not be the "best" solution, but it would offer you more protection than just one layer of poultry netting and it would not cost as much as many other alternatives.