in a sense, each head takes up a viewpoint on a situation and discuss it, just like how we try to decide whether we do something or not in our heads. my best guess is her individual heads are incapable of taking multiple viewpoints into consideration as we can, and she needs all three to think rationally. but even though her three heads are capable of independent thought, she is considered one entity.
So if I'm following the greek mythology inspired lore- Minerva is like the polar opposite of Cerberus, right? I honestly, don't know, this is the first time I've seen the character. But still, I think she's a very neat character. I just like cat-eared girls in general.
Actually, This story is only loosely based on Greek myth, meaning that any knowledge of actual Greek myth doesn't really apply here. In this continuity, Cerberus isn't the name of one three headed dog, the three headed dog species itself. Minerva is a Cerberus, and like all Cerberus, she was tasked with being a guardian of the underworld, until she came to the surface and fell in love with a superhero named the Werewolf of London Ontario. There are other plot points that make the story much less cliche than it sounds when I describe it, but telling them here would by spoilers. As for the male Cerberus in the background, he hasn't appeared in the comic yet, so we don't know.
If you wanna read the comic, you can find it here.