Electronically switched multiple BNC help?

Hello,
I am trying to do a measurement with a Parameter analyser from multiple devices that we place in a socket and connect to the parameter analyser through the BNC that connects to the Ribbon Cable (see picture, attached).

At the moment, we can measure a single device at a time.

Is there a way to make measurements from ALL of the devices in an automated way, that are accessible through the ribbon cable at once? With some sort of a multiplexer that takes all of the inputs from the ribbon cable, switches one-by-one and routs them to the single BNC output that will be recorded by a parameter analyzer? If this switching can be controlled for example by GPIB, etc, that would be wonderful.

Does anything like this even exist? Could somebody recommend where to buy such a "multiplexer" ?

Your picture and text does not indicate the signal bandwidth. There are multiplexer switches commercially available, see e.g. www.minicircuits.com. Their bandwidth usually covers DC to 4...6 GHz or more, and cost corresponds to it.
For bandwidth say to 100 MHz, you can find integrated circuits like SP4T. For DC to 10 MHz you can even use CD4016 or CD4066 CMOS analog switches.