How to prevent de-ranking of sites with duplicate content?

[minnow]

Hello, 

I have a long established site for my Australian business. I have just launched a dedicated site for North American customers. Taxation, banking, fulfilment etc all necessitate having two sites. 

I've duplicated much of the content across both sites. Both on pages and product descriptions. 

My Australian site is built on Woocommerce and my US site on Shopify. Given the ease of use of Shopify, I'm open to moving the Australian site to Shopify however I'm not in a position to upgrade to Shopify Plus right now. 

How do I prevent Google from de-ranking one or both sites due to this duplicate content?

And is there a Shopify structure for this sort of set up that I'm missing?

Thanks so much!