What if Quirrel can possess many bodies at once.

Then he would rule the world the day he decided to rule the world (which he did at one point, at least extending to magical Britain). A single Quirrell is among the most powerful wizards in the world. A team of Quirrells would have no meaningful opposition, even before he took advantage of the hive-mind benefits of instant coordination and reaction.

Being possessed of normal human emotions, his fondness for Harry could be real.

That would imply that all the words and actions that portray him as a sociopath are an act for Harry's benefit. What would his motivation be in doing this?