How about a Teensy reading the analog inputs of 4 of these over I2C
https://www.adafruit.com/product/732
But that is a MCP23017, which is digital only (i.e. with it you can do either digitalWrite or digitalRead, but not analogRead). I think you meant either the ADS1115 or ADS1015:
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But even so, you can only have 4 ADS1015 or ADS1115's on an I2C bus due to address limitations. That would at most 16 analog single ended inputs (or 8 differential channels).
You can go to an I2C multiplexer to get 8 separate I2C buses, but then the question is can you read all of the inputs with all of the switching fast enough that the human won't notice.
Now, a Teensy 3.6 has 4 I2C buses, so in theory you could get up to 64 inputs without using a multiplexer. Plus of course, the Teensy 3.6 has 25 pins that can do analog input (but 4 of the pins are used for the 1st and 2nd I2C buses).
The Teensy 3.5 only has 3 I2C buses, but it has 27 pins that can do analog inputs (and again 4 analog pins are used for the 1st and 2nd I2C buses).
I tend to think this is getting complicated, and it is better to have 8 cheaper processors that each have 8 analog inputs, and output via some communication method. I2C may be too slow, but perhaps using a UART line, and have the processor return all 8 inputs in one I/O (complete with a checksum).
Perhaps a Teensy LC for simplicity of programming, perhaps a raw AVR 328p chip running at 8Mhz and 3.3v. If you have more processors, each with 8 inputs, it becomes easier to test, and you can build a few spares, so that when one goes on the fritz, it is easy to replace 8 inputs, than 32.