I like to make small alterations to standard tuning that allow smaller intervals in the lower register.

Am9 (detune the D to C)

Some chords (note the 3rd intervals between the A and C strings):

Cm7 x-3-3-3-4-3
C x-3-4-5-5-x
Cm9 x-3-3-3-3-3
D6/9 x-5-6-7-0-0
A 5-4-4-6-x-x (or just 5-x-4-6-x-x)
A7 5-7-7-6-5-5 (standard E bar shape!)
Emaj9 0-9-8-8-0-0 (nice 2nd interval between the F# and G#)

D6add9 (detune the G to F#)

This gives you an open major 3rd interval and an easy D6add9 in the upper 5 strings. Some chords:

D6 x-0-0-0-0-2
G6add9 3-x-0-3-0-0
Aadd9 x-0-9-7-10-0
A6add9 5-4-4-0-0-0
A/C# 9-7-7-7-10-x
A13 x-0-5-5-7-0
Em x-7-5-5-5-x
Eadd9 x-7-6-5-7-x
D x-0-0-0-3-5  OR x-0-0-0-7-x
Gmaj9 x-5-5-5-7-5