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Hi,
Let´s assume an OPAMP with 10uV RMS input voltage noise.
And a +/-15V supply.
Maybe the max output voltage is +/-12Vpp.
This is about 8.5V RMS
at a (noise) gain of 10...
you will see about 100uV noise at the output --> 98.6dB SNR
****
Now double the (noise) gain by 2 and get 20.
You may expect about 200uV RMS noise at the output.
But the (usable) output voltage range will still be 8.5V RMS --> 92.6db SNR
Klaus