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I would like to scale multiple shapes, but locking the padding between them. Is this possible within Illustrator?
If you scale both shapes at the same time, they will stay the same relative distance to each-other.
If you don't want the (relative) size of the strokes to change,
Open the Transform Panel (Window → Transform or Shift+F8) and check Scale Strokes & Effects
You could use the object > path > offset option too. Just use the same value for both
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