As a passenger in a long car ride today, I decided to write out every possible 7th arpeggio that could be applied to degrees 7, 9, 11, and 13. Combining all possible alterations (b7/7, b9/9/#9, 11/#11, b13/13) yields 24 different ways to play these tones. Most don't make sense in theory and don't correspond to any common 7th chords, but might sound interesting in the right context. I'd rather focus on the ones I know I can use before exploring applications for the weird ones.

Here's what I wrote down. Arpeggio names in parentheses where common ones exist.

7 9 11 13 (m7b5)
7 9 11 b13 (dim7)
7 9 #11 13 (m7)
7 9 #11 b13 (m6)
7 b9 11 13
7 b9 11 b13
7 b9 #11 13
7 b9 #11 b13
7 #9 11 13 (7b5)
7 #9 11 b13
7 #9 #11 13 (7)
7 #9 #11 b13 (6)
b7 9 11 13 (maj7)
b7 9 11 b13 (7)
b7 9 #11 13 (aug7)
b7 9 #11 b13 (7#5)
b7 b9 11 13 (m/maj7)
b7 b9 11 b13 (m7)
b7 b9 #11 13
b7 b9 #11 b13
b7 #9 11 13
b7 #9 11 b13
b7 #9 #11 13
b7 #9 #11 b13

A few are appealing at first glance. Just looking at the most common jazz scales, 7 9 11 13 fits over Melodic Minor, 7 9 #11 13 fits over Lydian, b7 9 11 13 fits over Dorian, b7 9 #11 13 fits over Lydian Dominant, and a number of them fit over Locrian #2. With the arpeggios beginning with b7, you can take your pick of altered extensions over dominant chords.

It's always most satisfying when extended arpeggio fragments like these match up with common 7th arpeggios. Because b7 9 11 13 is a maj7 arpeggio starting on the b7, I don't have to learn any new fingerings. I still prefer to think in terms of what I'm playing over the real root (a major triad built on the b5 degree is really b5 b7 b9), but my fingers will remember the familiar fingering patterns.