As per an SPI test case, the single MISO-MOSI wire might work for beginning, then what about a bunch of shift registers, e.g. 74xx595?

yes some use non-SPI chips with SPI, however there is a difference:

A TRUE SPI chip will have a chip select that, if not asserted will put the chip in "pass through" mode. Thus, if you have a chain of TRUE SPI chips and only one CS is asserted, you will have the effect of 'talking to' one chip only.

On the other hand, if you use non-SPI chips ('normal' shift registers), you will need to produce as many clocks as there are bits in the entire chain to address any chip.

Erik