Well… if one must believe their own logo, (see sata-io.org) “SATA” shoud actually be expanded to “Serial ATA” :)

Acronyms of acronyms may not be super-common, but they do exist: eg. Cisco has a network protocol they call “PVST”, which means “Per-VLAN Spanning Tree”, where “VLAN” is “Virtual Local Area Network” (or “Virtual LAN”; LAN is another of those acronyms that is mostly regarded as being its own word).

In open source, there’s a long tradition of recursive acronyms: eg. “Linux” means “Linux is not Unix”, which you can’t in finite time expand according to your rule :)