Hi Michael,
Is there a schematic available? What part are you using?
I've attached a schematic from a board I use. It's got two 74HVC595
shift-registers cascaded, to form a really crude SPI expander; you
should probably ignore all but the shift-register interconnections.
These shift registers have two clocks (SCK and RCK); one shuffles data
through the shift register, and the other latches the current state on
the QA-QH outputs.
In this case, the Q'H output on the first shift register feeds the data
input on the second. It's pretty much designed to cascade registers this
way. The separated clocks allow data to be shuffled behind the scenes,
without affecting circuitry attached to the outputs. I'm guessing parts
are probably similar, since it seems like an obviously useful building
block.
best,
Graeme