Woocommerce – shop page to show in and out of stock

Hey all,

Anyone can help with coming up with a way to do the following:
– By default, I’d like the shop page to list all products, both those in stock and those out of stock. This i can do already.
– I also want to give customers the options to switch to a view of only products in stock.

Is it possible to do this maybe with the press of a button by the customer ? Ideas of how to accomplish this are highly appreciated.

Thank you,
Mihaela