Tomcat as being a barebones servletcontainer provides indeed only JSP, Servlet, EL and WS APIs out the box. You can however just provide JSF, JSTL, CDI, JPA, Hibernate, Spring, etc yourself along with the web application in flavor of JAR file(s) in the /WEB-INF/lib folder and some configuration files where necessary.
EJB is only a story apart since you can’t just add “some JARs” to get that to work, but in fact yes, you can put an EJB container on top of Tomcat too if you modify the server core. That’s also basically what TomEE has done. You might as well consider it if your intent is to go Java EE.