Shift registers in series
You are correct.  So long as the Dout of the first shift-register is routed into the Din of the 2nd, and then from 2nd into 3rd, and as you say have Latch, Clock &amp; OE of all 3 connected together &amp; into your MCU (or whatever you're driving them with), then you can clock in 48 bits, and then latch &amp; OE them all at once.  What ever was in the 3 registers originally 'disappears' (virtually 'falls out the end' of the 3rd shift-register's Dout pin) SO LONG as you clock in all 48 bits.

Alternatively, you can choose not to clock all 48 bits, for example in a LED display - with this technique you can achieve 'sliding' effects without having to re-clock all the 48 bits (followed by Latch &amp; OE) over &amp; over.  You can clock just a single new bit in (which pushes the 48th bit out the far end never to be seen again), and then whatever was originally in the 48 bits shifts over 1 bit - whatever 'pattern' that might be shifts over 1 bit, &amp; a new bit is added.  I'm probably not explaining it very well, but just give it a try, you can't hurt anything :)