Translation:I want to know as many languages as possible.
With "co" it is about me only. Without "co" it is about comparing with another group of people: I want to know the the highest number of languages (of my classmates) / (to create a new WR)
So, after a few sentences like this, I think I see a pattern that suggests that "co (some superlative)" is a phrase that means "as (whatever) as possible." Is this right, or I am grasping at straws?