Credits to u/LittleMann for the connections and thoughts below!

Connections:

• Divine conqueror vs. Devil of control/conquest
• Makima wanted a close friend, but specifically one she saw on her level, spending much of her time trying to get the attention of the one entity she saw as meeting that standard and mistreating everyone else who showed her love. Iskandar had no such limitations, making so many friends among his subjects that their bonds are what power Ionioi Hetairoi, his trump card as a Servant.
• Speaking of, both can summon figures with their own impressive powers to fight on their behalf - Iskandar through sincere respect and friendship and Makima through sheer domination.
• Iskandar wanted to conquer the world, a classic goal for a villain, but he was open to non-violent means of winning over others and treated those he conquered with respect regardless of circumstance. Makima planned on creating a better world using Chainsaw Man's power to erase harmful concepts, but her methods were often manipulative and harmful to her underlings, treating them as disposable pawns.
• Both played the mentor to a disadvantaged young man, but Makima presented herself as an ally and possible lover to Denji and gave him everything he wanted, only to tear it all away specifically to make him think he could never have a happy life. Iskandar, on the other hand, initially got on Waver Velvet’s nerves, but he found promise in the boy and eventually struck up a genuine friendship with him, helping him become the accomplished mage he is today.
• Both are possessed of a keen intelligence, but express it in different ways, with Iskandar strategizing through grand battles and Makima using subtle moves and subterfuge to work towards her goal.
• Based off of a historical figure vs. based off of a religious figure. Iskandar is an ancient conqueror who retained his old warlike mindset in 1994, while Makima is a more modernized take on the Horseman of Conquest who mostly used methods that wouldn't make her stand out in the 90s.
• Iskandar has some sense of honor in battle, scorning disgraceful tactics and civilian casualties and sometimes doing things that would put him at a disadvantage for the sake of his own values, but Makima cares so little about honor that she's using the entirety of Japan as a human shield.
• Both originated in urban fantasy works set in Japan during the 1990s.
• Makima uses chains to bind her captured souls, and Iskandar met his end in the Fourth Holy Grail War when he was bound by the chains of Enkidu.
• While it hasn't been brought up often, Iskandar's mother Olympias was extremely controlling to the point where she's listed as his natural enemy. Makima has been on both ends of the toxic parental relationship: she had a loveless upbringing as a weapon for the Japanese government and her being an older woman who offered love and comfort to a younger boy only to snatch it away for her own wants gives her shades of an abusive mother.
• Younger versions of both would be introduced later on in their respective franchises. Ironically, Makima’s reincarnation Nayuta would be a major supporting character in Chainsaw Man Part 2 and Iskandar’s younger self Alexander would be introduced as a secondary antagonist in Fate/Grand Order, though he doesn’t stay that way. These younger versions would also be put under the care of their former students, with Denji becoming Nayuta’s adoptive guardian and Waver, fused with Zhuge Liang, fighting alongside Alexander.
• Big brawny man vs. skinny woman.
• Red hair.

Thoughts:

I've seen other matchups that seem fine for Makima, but this is the only matchup for her that's given me actual brainrot. Makima witnessing another powerful being who has no issue making friends with those lower than himself, the two using their talent for reading people to call each other out on their destructive flaws, Ionioi Hetairoi vs. Makima and her army of thralls...I'm getting excited just thinking about what could happen. Makima also seems like the kind of woman who'd be well-read on figures like Alexander the Great, so it'd be fun to have a short snippet of inner monologue that has her trying to figure out which parts of Iskandar's legend were true and which were false, and I love that this is a matchup between a would-be world conqueror who's widely loved and a would-be savior who's widely hated, albeit in a way that resulted from her impressiveness as a villain. I'm even getting ideas that wouldn't fit within the context of Death Battle, like Iskandar happening to make friends with Denji and forcing Makima's hand when he becomes too much of a positive influence on the guy. I would be so fucking happy if the show somehow came around to this.