The problem you describe is most common within manufacturing and assembly facilities.

You can put a bunch of BOMs with each item as a line in an excel spreadsheet and then find what parts have the highest counts. This may help you elicit some helpful or interesting information.  But this can also be misleading. 

Most manufacturing is component based.  So a large product is made of of many components which are each made up of a series of individual parts.  You want to create kits that easily roll up to components.

So each kit would build a component.  Of course you may be able to take this a step further and find a common combination of parts that are used in multiple components. That way kitting the components will be even quicker since it's a kit of a kit. IKEA does this.  When you get a bunch of piece of hardware for your furniture, usually you open one plastic bag to find 10 other smaller plastic bags.