256 : 1 or 64 :1 or 32 :1, 5v multiplexer to handle 256 analog signals
You can use 3 pins (2 with some cleverness) to control a 74HC595 shift register. The shift register has 8 bits, which is sufficient to address 256 inputs.
You would feed 4 bits to 16 74HC4067 or similar and the other 5 bits to a 1 low of 16 decoder, such as 2x 74HC138, and use those outputs to enable the '4067 chips.

There are serially controlled MUX chips such as the 32:1 ADG731 32-input chip however they are higher performance, sometimes better protected, and tend to be more expensive (and perhaps may suffer from availability issues in the future). To use the required 8 chips you could use a 74HC138 as the selector. You'd need the three address pins plus the 2 + 1 SPI pins for a total of 6 pins.
As a rough comparison, USD Digikey price for Q100 each of the first solution is $8.28 vs. $89.40 for the second. Or if you prefer LCSC, $3.17 for the first one.