They are analog switches, so in principle you can tie their switch commons together (they don't have 'outputs' as such). However, if you tie them you'll need individual /E lines for each '4067 so only one is active at a time , though you can save threeMCU pins by using a 74HC138 3 to 8 line decoder to generate the six /E lines from three select lines. S0 to S3 on all the '4067s can be paralleled like for like, so a total of eight MCU I/Os will be required, seven outputs to address a specific input channel and one ADC pin.
That's only a saving of two MCU pins compared to the four outputs required to drive the Sn lines in parallel and six ADC inputs , keeping the '4067 switch commons separate and assuming its acceptable to keep the /E lines grounded .
Both solutions assume its acceptable for switching glitches to briefly short two sensors for as long as it takes the new input selection to propagate through the '4067 internal logic. If you must guarentee break before make, you'll need a master /E signal so you can disable all the '4067s before changing the input selection control lines. Wire it to the '138 if you tie the commons together to one ADC pin or to all the '4067 /E pins if using separate AC pins.
N.B. the single ADC pin arrangement will have slightly worse crosstalk and noise than separate ADC pins. It shouldn't matter if all the sensors are similar, low impedance and don't have HF noise on their outputs.