Adding fields to shop page

This is my first Woo site, for a client that has a lot of mechanical parts, many with the same name, ie “gauge” or “bushing” etc. I would like to add one or two additional fields for the shop page. Right now there is only the image (which I’ve removed), price and “add to cart” link.

In looking at the woo commerce products tab, under manage imports-edit options-general, there are several fields (sku, price, sale price, tax etc) but that seems to be it, AND I can’t even get the sku to display.

So my question is, is there a way to add another field or two that will display on the shop page or do I have to resort to creating overriding files and adding in new field functions?

(and why doesn’t sku work?)

Thank You.

https://www.ads-software.com/plugins/woocommerce/