Playing major, minor, 7th barred chords on all fourths tuning is trickier than standard tuning. However, when it comes to more complex chords, it offers more options.
Major barred chords
You can choose to play or mute the 5th string. The middle finger is used to play the root on the 6th string, it can slightly touch the 5th string to mute it. These shapes can be moved to play with root on the 5th string.
Maj7 barred chords
Similarly, you can choose to play or mute the 5th string. These shapes can be moved to play with root on the 5th string.
Dominant 7th barred chords
These shapes can be moved to play with root on the 5th string.
9th chords
7b5 chords
This shape is movable to other string sets, e.g. root on the 4th or 6th strings.