Here are open and close position 7th chords with the 1st and 2nd open strings added.

6th String Roots:

5th String Roots:

Remember: these shapes should be played at every fret in order to find the ones you think you can use. Maybe someday I'll create a table that lists the name of every one of these shapes at every fret - or not! Better yet, study the system of theory I teach in my book, Vertical Truth - Chordal Mechanisms for the Guitar, Units 1 Through 10, and you can figure out the names for yourself.

There are many, many more shapes possible. For instance, on the 6th string roots you could add the 5th of the chord on the 2nd string - or the flatted 5th - or the sharped 5th. On the 5th string roots the 9th could be added on the 2nd string - or the flatted 9th - or the sharped 9th. Here are just a few random examples of what you can find if you think about it for a while.