It sounds like you are wanting to send some extra data to the page you are redirecting to. No, this isn't possible outside of the query string. You should understand what is happening here.
When you send a 302
or 301
status code along with a Location:
header, the browser sees this and then makes a separate request to the URL specified by the Location:
header. The server isn't sending anything to that page. It's almost as if the user simply typed in that new URL in their browser.
I say almost because in some circumstances, there is a referrer set by the browser. This isn't guaranteed though.
What you can do is send some sort of token that contains more information. Perhaps your page saves off a message in a database or something, and then you pass the ID in the query string of the URL you're redirecting to.
Also, if you set session/cookie data and you're redirecting to something on the same domain, you can read that information on the page the user eventually lands on.