Abbreviations

Q. Is it proper to define an acronym within an acronym or an abbreviation within an abbreviation? I am working on a document that contains an abbreviation that is really two other abbreviations smushed together with additional words tacked onto either side. And to top it all off, the overall abbreviation doesn’t even contain the first letter of every word in the other two abbreviations. They’ve dropped letters to make it shorter. Finally, if it is acceptable to do this sort of thing, how would I define the abbreviation or acronym on first use within the document if the two incorporated abbreviations were not previously defined in the document? Whew!

A. Who wrote this document—Dr. Seuss? Yes, you may explain this funny animal parenthetically regardless of the lack of previous explanation. And maybe you should hire a cartoonist to illustrate.