How do you use output redirection in combination with here-documents and cat?

Let's say I have a script that I want to pipe to another command or redirect to a file (piping to sh for the examples). Assume that I'm using bash. I could do it using echo: echo "touch somefile echo foo > somefile" | sh I could also do almost the same thing using cat: cat somefile EOF But if I replace "EOF" with "EOF | sh" it just thinks that it's a part of the heredoc. How can I make it so that cat outputs text from stdin, and then pipes it to an arbitrary location?