I'm one of the few who think that Sasori has very good assets to counter Itachi.
He's a robot with just an organic heart, so I see him as insensitive to genjutsu. His robot body won't make him feel the pain of Amaterasu's flames and we know that those flames take time to completely char their prey. For me Sasori will have time to switch his heart into another puppet (he did it instantly against Chiyo and Sakura, so it acts like a teleportation) he can summon.
He has all kinds of traps and vicious attacks (the puppet movements, omnidirectional attacks will be difficult to anticipate for the Sharingan. It's not human movements, it's Kugutsu), all poisoned, he has the Iron Sand which is a weapon of death (and poisoned too)
that can be very fast and magnetize you. And he can probably even use IS in defense (even if it's not as good as Gaara's).
I hope that P1 Itachi has much better reflexes than
P2 sick Itachi who got hit by the trap of Sasuke's Shuriken Fuuma (I know Itachi manipulated the fight but I see no reason to be trolled by this attack) otherwise he will end up poisoned. It's too risky to go and attack Sasori in hand-to-hand combat.
He'll have to use Susano to protect himself (hoping that Sasori can't use Iron Sand in a way that the sharp attacks go underground and then under the Susano).
If he manages to resist for a long time in Susano (so he will be able to counter the 100 puppets), to hold, to hit with Totsuka then he'll end up beating Sasori (I don't see the heart switch trick working forever) but it will be very hard since even in P1 (who was quickly fatigued after 2 Tsukiyomi and 1 Amaterasu), I doubt he'll have a lot of stamina (Sasori has a lot more).
IMO Itachi high-extrem diff Sasori in 1 vs 1 (Sasori can even win in some cases. Sasori is an underatted character because he "lost" against Sakura/Chiyo but he had plenty of mitigating circumstances. I consider him a genius with a huge potential. I could talk about him for a long time, so I won't go into more detail).
So Itachi can win against Sasori but Kakuzu is added and for me it's becoming impossible for Itachi. Kakuzu has several masks/lifes in him, maybe it could help him to break the genjutsu. Itachi will have to kill him several times even with MS (which will make him spend a lot of energy and knowing that Sasori is there too). Moreover when we saw that Danzo's Fuuton could create an opening in Sasuke's Susano's back, maybe Kakuzu and his Fuuton combo will be able to do the same in Itachi's Susano's back. Of course I know that Itachi's Susano is a superior version of MS Sasuke's, and there's Yata who can block everything (but can Yata cover all of Susano ? The bacl ?) so it's unlikely to work for Kakuzu.
Nevertheless, Kakuzu, his ninjutsu, mask/lifes, experience (to me being trolled by Naruto strategy was PIS), should give Sasori the help he needs to put even more pressure on Itachi and force him to burn out even more.
So I see him running out of chakra before he can defeat his opponents.
Duo high diff.
Edit: For me Izanami won't be of any use here. Sasori and Kakuzu don't have the required personality (they're not trying to pass themselves off as someone they're not like Kabuto) and then it's not easy to throw (you have to create two identical situations for the loop) especially at 1 vs 2. And then you lose the sight in one eye.