So Iceborn seems to be a thing now with Jax, and it offers a perma slow. So I am thinking maybe Liandry's will make a good combo? We all know Jax is good with AP, and the passive is pretty amazing. He will be doing a lot of magic damage, and I think you don't need to be doing CONSTANT damage since the effect lasts 3 seconds, so as long as you are doing magic damage every 3 seconds, you are good, right? So it essentially adds a 5% damage DOT to your Empower? The thing about Liandry's is that it states it does double damage to someone who is slowed, and you should have people perma slowed with Iceborn, turning it in to a 10% damage on empower.
I am thinking:
Mercs Iceborn Rageblade Gunblade Liandry's Black Cleaver FOTM?
Also with the way that penetration comes AFTER %, I am thinking of running split pen reds and then taking both the arm pen and magic pen masteries, giving him a total of 26 flat arm pen, 8% arm pen, 30% from stacked cleaver ( super easy with jax ), 20 flat magic, and 8% magic pen. More if you go with split pen quints as well. The split pen needs to be tested, but it seems like they are a great option now.
Also has 25% CDR with no masteries, so there is room for a blue elixir, baron, or sometimes even that blue steal.
you can just get BORK and TF and people still probably won't be getting away, I don't think the supposed perma-slow on icyhands makes it worth it. I'd be interested to see if the mana+ap+cdr+armor proves more useful than TF at any point. It very well might.
If the math supports the liandry's burn+permaslow being higher damage than other options I'm all behind it, thing is I'm not sure if it does.