Generating Inverted Signal with 74HC4067

I have a system where I have a 328 hooked up to a 74HC4067 in order to talk to 16 sensors over SPI. The lines of the mux are connected to the slave select pins on each of the 6 sensors, so I can choose a sensor to talk to and transfer data. The only problem is, slave select is disabled for a high voltage and enabled for a low.

As a result, I am looking for a way for the mux to output a high signal on all pins BUT the one I have chosen. Essentially the inverse signal. What I'm seeing in the data sheet is for a chart that does just that, but I'm not sure how to get it. Any ideas?

Thanks!
DC

Pull up resistors?

on each line? There's no way to configure the 4067 without 16 pullups?

on each line?

Yes

There's no way to configure the 4067 without 16 pullups?

No way.

It strikes me you are using the wrong chip here.