Can I create multiple invoice templates that each have a unique email message?

Hello there, useraccounting6.

If you mean editing different messages of each template, the newly modified message in the template takes over and replaces it with all existing invoice template messages. Other than that, you can customize the template without affecting others. 

And yes, you can create unique messaging by importing your own design. We can download a sample template within your QuickBooks Online account. Here's how:
 

1. Go to the Gear icon.
2. Select QuickBooks labs and click Import style.
3. Open Custom form style and select Import style by clicking the New style drop-down arrow.
4. Select the type of transaction you want to use.
5. Click Download a sample file. 
6. Open the downloaded zip folder and open the sample document. 

When creating a template, make sure to your message in the Message field. Then, import it to the program. For more details and tips, please check this article: Import custom form styles for invoices or estimates. 

Also, check this one to get more details about customizing sales form, and email sales forms to your customer: Send sales transaction to a customer. 

Let me know if you have other questions. Take care always and have a good one!