A couple of colleagues and I have been going through some Google NGrams. At first it seems quite conclusive that plundering is a far more sea worthy activity than pillaging, and plundering is certainly the more pirately thing to do:
In an actual example: British critic: and quarterly theological review, Volume 16 (pp. 516 to 518), they appear to use pillage and plunder interchangeably as nouns, but only plunder as a verb. This seems fitting for water-borne criminality.
In this discourse of plunder (page 2) pillage is said to be something that makes up plundering.
However, the further I read into the samples provided by the Google book search, it seems that pillage and plunder can be used interchangeably, it's just that plunder is a far more popular word.
In fact, although it is a much rarer occurrence than "pirates plundered", "pirates pillaged" does appear in literature. Some examples:
Outside of buccaneering, there is a lot of synonymous usage of plunder and pillage - here are some examples:
In a text about the history of English government, on page 94 they write:
Commercial plunder, however, was to be more destructive than military pillage
On page 554 of The new encyclopædia; or, Universal dictionary of arts and sciences they define Pillage by using plunder. An later on page 687 they define plunder using pillage.
There seems to be no difference in the meaning of the two words in The works of the Right Honourable Edmund Burke, Volume 7 on pages 408 and 410
Again I find the same in "The Forum, Volume 17" (plunder, pillage)
So, in conclusion, it seems that plundering and pillaging are the same thing.
I'd say you are wrong.
To ambulate is to move by means of walking, parallel to the way brachiate means to move by means of swinging with your arms from hold to hold.
To perambulate is to walk through, or to traverse, something. Perambulate therefore can take an object to be traversed. You can "ambulate idly all afternoon", but rather than "perambulating idly all afternoon"; you should "perambulate the yard idly", or some such thing.
Best Answer
There are two different idioms here, and you may be confused. In Don't all speak at once, all and at once are separate, and both modify speak; the normal rules apply to all/both, as Barrie has said. But all at once can also be a single phrase, where all intensifies at once ("When all at once my heart took flight", My Fair Lady). I don't believe there are any rules for when you can or can't use that.