I have Arduino Mega 2560 with MuxShield II on top of it and two (as for now) SHT75 sensors (datasheet, library) connected. The problem is that the Sensirion library has default constructors prepared to work out-of-the-box w/o a shield so I had to make changes: I've added a pointer to the MuxShield object to each Sensirion object and swapped the latter's read, write and set pin mode operations to these provided by the former. Now I'm getting "no response (ACK) received from sensor" and "CRC mismatch" errors and obviously a rubbish output. I'm pretty sure that everything's connected correctly. My code is here but I don't expect you to debug it. But what is a general approach of using multiple sensors with shields?
The pullup handling is not done correctly. You cannot activate the internal pullup for every pin separately with your mux shield. Try to set the complete row to DIGITAL_IN_PULLUP instead of DIGITAL_IN and set DATA_PU to 0.
But what is a general approach of using multiple sensors with shields?
There's no general approach because it differs from sensor to sensor and especially MUX shield to MUX shield.