Back grads are critical, edges are not. Where the plate is glued to the ribs/linings, thickness and stiffness are not important within normal limits. It would waste your money to regraduate the back plate again for that reason.
As a matter of fact I think the best possible way to graduate the back would be from the outside after the instrument is fully strung. But that has nothing to do with your question.
What exactly are you thinking you might want to achieve by this regrad?
Someone with a few basses could try this experiment of give and take. Tap the back at the point where the SP is situated with a thump of the finger. Listen for the sound level of the open strings. Now repeat with a couple other basses and relate this to their sound level, loudness, punchiness (not necessarily timbre) . A stiff back can prevent a bass with a perfectly good top from sounding loud and responding to the bow well. Now reverse this in your head as you imagine the sound starting at the string, through the bridge, rocking the top, causing the post to move the back.
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