Is the PayPal REST API designed for a single developer (or application) to interact with multiple PayPal accounts? Or can only PayPal partners do that?
Specifically, I am developing a software product (SAAS application) for small businesses that generates invoices among other things. Can I use the PayPal REST API to email invoices on behalf of each of my small business customers?
You can do this, but you would need to integrate and setup third party permissions with each merchant, basically a way to ask the merchants permission to do what you want to do, see here for the details:
