How could you do that? The Borg aren't characters. The Borg are one character. Every drone is a cell in a single collective mind, robbed of all autonomy and self-awareness. You can't tell much of a story about a single character, especially one with such a rigid thought process, driven by an instinctive need to expand and absorb. Really, the Collective is barely even a character -- it's more a force of nature, a cancer spreading across the galaxy, or at least it was until the Queen was retconned into existence as its face and voice.
That's why most every onscreen Borg story after the first one involved individuals who were taken as drones or liberated from being drones, or about the civilizations that fought the Borg or were destroyed by the Borg. Stories need to be about people, not impersonal entities, and so they had to work around the concept of the Borg in order to include characters in the narrative. Because, frankly, the Borg were not a great idea. They were a great idea for a single story, but the original concept was so dramatically limiting that they had to change it and work around it in order to get any more stories out of it. The only interesting stories are about the victims and survivors of the Borg, or the origins of the Borg. And all those types of stories have been told already.