For diatonic scales, I use a system that is primarily 3 notes per string (or shift). To do this, you have to realize that there isn't a single box for a given scale/mode. Instead, there are multiple patterns (shapes/boxes) for each scale/mode.
For example, in this approach a major scale can start with 1st finger, or 2nd finger, or 4th finger. This means 3 different "shapes" for a major scale. I think most people (I used to be among them) get stuck in the box that starts on the 2nd finger. As you expand, though, you realize that this box ends on the 4th finger, so you can continue with the next pattern (starting on 4th finger) and repeat the scale. The major scale that starts on the 4th finger ends on 1st finger. The major scale that starts on the first finger ends on the 2nd, and you're back to the where you started.
As you move from one of the 3 note patterns to the next, you can move up (or down if you're playing descending) a string, or you can shift, but the pattern continues. Over time, your mental representation of the patterns will begin to expand to cover the entire fretboard.
In this video, Anthony Wellington shows how to apply the patterns to modes on a 7 string bass. You don't have to have a 7 string bass to use it, but it makes an interesting point.
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Obviously, my post isn't a lesson on scales. I'm just pointing in the direction of the approach that I'd use to answer your question about how to expand scales to more than box shapes. It starts with a box shape, then expands it to multiple shapes, then it expands to patterns across the fretboard. Eventually, the boxes fade and it becomes notes, in convenient and accessible patterns.
Wow. Thanks for sharing this.