Is this sentence correct?
The story must be as much realistic as possible.

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The story must be as realistic as possible.

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The story must be realistic as much as possible.

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much signify the extent/to the full  of something... 
in the sentence "as possible" is also expressing the extent of the reality the story needs.

Here is a way you can use Both much and as possible in the same sentence.
1 Can you make the story realistic as much as possible please? 
2 The story must be as realistic as possible.

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Thank you!

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The story must be as realistic as possible.