Watch the Applying The Box Amaj7(#11) online guitar lesson by Robbie Calvo from The Power of Five
The major 7 (#11) chord typically and diatonically functions as a naturally occurring IV chord in any given major scale key. It can also function temporarily as a I chord. In this example it is actually functioning as the IV chord from the key of E major. I can determine that easily by looking at the other 2 chords in the progression.
Our tonal center is the IV chord and I'll be applying 3 minor pentatonics over the progression to create some nice melodic flavors. My first choice over this Lydian based progression is to apply the G#minor pent. This scale will give me that lovely D# that defines the Lydian sound of this progression. I'm going to milk that note for all it's worth.
The G# minor paired with the F# minor pent will work really well and you'll be able to glide between the 2 positions using our one shape with relative ease. Use your ear to determine sweet notes and remember where they are within each pattern.
The C# minor pent works beautifully over this whole progression and you may just want to hang out here for a while creating some subtle lines that flow across the musical landscape.
Try mixing your phrases and lead lines between all three positions and utilizing the same lick to create motifs and hooks simply by moving your shape positions.
Let's analyze the chord scale relationships
Ama7(#11) = A-C#-E-G#-B-D#
G#min pent = G#-B-C#-D#-F# = 7th-9th-3rd-#11-13th
F# min pent = F#-A-B-C#-E = 13th-R-9th-3rd-5th
C# min pent = C#-E-F#-G#-B = 3rd-5th-13th-7th-9th
Take note - these scales all work well but not all of the notes are good resolution points over each of the chords. Use your ear and note knowledge to phrase lines that resolve to the sweet notes of each chord or the tonal center.