Is it possible to build an eCommerce website with Elixir and the Phoenix framework?

Yes, but why? This is mostly a solved problem already. Especially if you only have a small amount of SKU’s.

What I would do instead, is to use another engine, but then run Elixir software to enhance it. Example, provide newsletters, more detailed user behavior profiling.

Most eCommerce engines go the easy 85% of the way that would super-tedious to build. So why spend that 85% again.

The value in Amazon are things like:

1. Recommendations
2. Those emails that remind you to buy
3. Affiliate marketing

Use Elixir/Phoenix to add it those parts instead.

1. What popular or emerging web applications are built with the Elixir language and Phoenix framework?
2. How much of the "Programming Elixir" book must I go through before I can start learning Phoenix?
3. Conditionally render templates in Phoenix - Elixir
4. How do I learn Phoenix (Elixir) in a pleasant way?
5. Is Elixir + Phoenix worth learning when you have to create very quickly web backends that scale to millions of users?
6. How mature is Elixir?
7. What can I do with Elixir?
8. Is Elixir (programming language) dying?