With the CAGED system for major seventh chords you can play any major seventh chord in five different positions on the guitar fretboard. If you haven't already, please have a look at the introduction of the CAGED system.
The CAGED system for major seventh chords uses the open major seventh chord shapes CM7, AM7, GM7, EM7 and DM7, which haven't been introduced so far.
Major seventh chords contain a major chord plus the major seventh. They have much less tension than the (dominant) seventh chords and sound like Jazz, probably because they are often used in Jazz music.
Here are the five major seventh chord shapes combined on the fretboard:
Below is a list of chord diagrams that result when applying the five major seventh chord shapes to the root notes C, D, E, F, G, A and B. Here is help on how to read chord diagrams.
Keep in mind that it's often possible to change the chord shapes slightly, e.g. by omitting duplicate notes or by adding an open string to the chord shape (for example, when using the D major seventh shape to play an E major seventh chord it's possible to add the low E string - this is indicated by the grayed out letter at the bottom of the chord diagram).
Also not shown below is that some barre chords can be played with the thumb over the neck instead of barring the strings with the index finger.