A real world example of this would be like the old phone exchanges
It's a bit different because the multiplexer handles analog inputs, but a port extender basically just outputs low or high. I suppose it depends on your definition of those words.
if you have 5 input and output lines I would like to be able to change how input pins are forwardedto the output pin.
This is more an app for a crosspoint switch, you can get them in 8x8, 8x16 etc. An 8x8 is basically 8 8-way MUXes in a single chip.