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You will have more samples and the result will be more accurate ie will closer follow the input signal.
The Nyquist cryterion only tells you what is the minimum sampling frequency and if your system is capable of taking samples more often or you require better resolution you can always increase the frequenco above the minimum 2 times ..
maybe you can use this advantage to help your work. One example is oversampled ADC, by oversampling input analog signal, we can simplify later design works.
oversampling also helps with digital signals in noise by providing several instances of the message symbols instead of just one. In a frequency selective channel, it helps by being able to use Fractionally spaced equalizers.
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