JWTs have 3 parts:
Is it possible to
In fact there is not only signed JWT, but several technologies described by RFCs:
In your case, read the RFC7516 (JWE). These JWE have 5 parts:
Depending on your platform, you may find a library that will help you to create such encrypted JWT. Concerning PHP, I am writting a library that is already able to load and create these jose.