Hi DigitalElise ,
Thank you very much for your post and question.
The free version POs work the same way as WooCommerce orders. You need to do things manually as you do when you ship a partial order to your customer.
You can either create a new PO with the inventory that has already arrived and modify the original. You could use the stock logs too where you create the partial delivery and press the add to stock button.
We are about to start development of a premium add-on called Ordering Premium in October. Here we will cover partial POs within the add-on.
Hope this help.