Create New Feature Class Based off Multiple Feature Classes

I've searched previous posts to see if anyone asks a similar question, but I haven't found anything. I have a multiple feature classes, each containing multiple polygons. I have two desired outcomes:

A) I would like to find any easy way to create a new single feature class in areas where more than 50% of my input layers intersect. The number of input layers I have will vary, but let's use 6 as an example. It would be nice to be able to create a single feature class no matter which of my four input layers make up the more than 50%. I've tried to create a model using Intersect, but I am missing the logic piece that tells the system that not all 6 inputs need to overlap, just at least four.

B) The other output I would like to have is a new feature class which creates new polygons which are an average area based off my inputs. In this case too I would like this tool to create a new feature class with the mathematical average of areas where more than 50% of my inputs overlap. I've searched, but cannot find any such tool that can get me at my output.

I currently have an ArcInfo (Advanced) license, but no extensions. If there is a way to accomplish my goals with either ArcView (Basic desktop) or ArcInfo that would be preferred. But if there is an extension out there I would be curious to know what it is.

Thank you,

JR