cmrr of differential amplifier
You will get the best signal-to-noise ratio by measuring at the highest permissible cmv. Also, it's unnecessarily complicated to sweep the cmv and evaluate the resulting cmrr curve because it is likely that cmrr will be well represented (with the very best snr) at a single, high cmv.
So, simply apply the maximum cmv to both inputs (which should be shorted together) and measure the output, then compute the cmrr as described in earlier posts.