Don't look for general stuff. Look for multiplexers/switches designed for particular port types.
Yes, having read about that in the
Texas Instruments Application note -Multiplexers and signal switches glossary document I further looked up
Texas Instruments' protocol specific switches and muxes, but it appears they only cater for currently used computer ports (USB, HDMI etc.).
And web/forum info on the subject seems quite complex, but I'm quite possibly looking up other scenarios in my ignorance, adding to the confusion

In my case they're ports on an Atari STe (80s/90s vintage computer), and I'm not totally sure if Atari followed established protocols back then either. I know for a fact that some of the ports were "almost" up to standards (like the video output which is "almost VGA", and the ACSI hard-disk port which is "almost SCSI"), so protocol specific MUX chips might not be the solution here? ......
Here are the specific ports I want to add switching to, and how:
1. Atari modem (serial) portA serial to MIDI converter will be attached here. But I also want to be able to occasionally use the serial port as normal -hence the need for a 2-way switch.

(Serial pinout source:
Info-coach)
2. Atari cartridge portThis port will connect to multiple hardware add-on expansion devices and copy-protection dongle cartridges. Unfortunately they don't all work well together (and frankly, I don't even need to have them all available at once), so I've grouped them into chains that do work. I also have an empty cartridge port for attaching whatever I need at the time. So here I want to switch to whichever cartridge "group" I need to use, hence the need for a 4-way switch.


(Cartridge pinout source:
Info-coach)
3. ACSI (hard disk) portACSI (Atari Computer System Interface) is an "almost SCSI" standard. I will attach an ACSI to SCSI interface to this port (so as to be able to use standard SCSI hard drives etc.), but I also want the option to occasionally use the port as the original ACSI (some add-on expansion Atari devices utilize ACSI), hence the need for a 2-way switch.


(ACSI pinout source:
Info-coach)