Software to connect to different marketplaces

I'm working with a person that has a wide variety of products he sells - watches, Amazon returns, sneakers, etc. He primarily sells on ebay, FB, and sometimes to other marketplaces.

Is there a website partner - WooCommerce, Shopify, other that we can list all the products on and then easily have them cross posted on the different marketplaces? And when things sell, they automagically get pulled and no longer appear on any of the websites. I just want one central place where things are organized and then have extensions to the other marketplaces.

Any recommendations for a service/website like that?