[Radio Wrangler]

The upper multiplex chip in that diagram switches only the shunt part of the feedback scaling resistors, and so the Rdson of the actual switch elements appear in series with the shunt resistor. This will act to lower the opamp gain, not increase it. To increase the gain would need either a wrong gain-setting shunt resistor or else some leakage path across that resistor.... maybe a failed-shunt ESD protector?

Alternatively, Rdson could have gone high on all the channels other than the high gain ones, reducing their gains.

Having Rdson get in on the gain setting act is not good design practice. There are well known ways of avoiding this.

David