Hi Phil, sounds like you are a little confused.
MOSI would only connect to the first shift register. The "data out" pin of the first shift register connects to the"data in" pin of the second and so on for as many shift registers as you like. The SCK and SS pins connect to all shift registers in parallel and here is the problem. The Arduino pins for SCK and SS can only connect to maybe 10 to 20 shift registers. More than that and the signal becomes degraded and the data cannot pass reliably. So you need some "buffer" chips to relay the signals.