Phoenix is already a lightweight framework
We do have other frameworks in Elixir, but I would say that generally they exist to offer different styles of development.
Also, in case you didn’t know, Phoenix has been described as ‘more than just a web framework’ in the sense that it can be used as a thin layer inside an Elixir app… multiple times
If that interests you, the legendary Dave Thomas goes into detail about it in his online course.