As I researched intervals further I found that some interval shapes remain constant as you move to most other string sets:
(A and D; A and G; D and G; B and high E).
However, when the lower note of the interval is on the G string, or if the G string separates the two notes of an interval, the shape changes.
This is due to the tuning of the guitar. Remember, the strings are tuned in 4ths except for the third and second strings, which is a major 3rd.
Below is an example of these interval shapes: