Meaning:
Make every possible effort.
Background:
The popular belief is that this phrase derives from the manner of
construction of pipe organs. These instruments have stops to control the air
flow through the pipes and pulling them out increases the musical volume.
This seems to be the type of casual easy answer that is the hallmark of folk
etymology. In this case, the popular belief isn't a fallacy but is in fact
correct.
Prior to the introduction of pipe organs the word `stop' had, in a musical
context, been used to mean `note' or `key'. That usage is recorded as early
as the late 16th century, as in this example from George Gascoigne's satire
The Steele Glas, 1576:
"But sweeter soundes, of concorde, peace, and loue, Are out of tune, and
iarre in euery stoppe."
Of course, `notes' and `keys' can't be pulled out. The word `stop' later came
to be used for the knobs that control the flow of air in pipe organs, by
pushing them in or, more to the point here, pulling them out.
The first person to have used the phrase in a figurative, that is, non-organ
related, sense appears to have been Matthew Arnold, in Essays in Criticism,
1865:
"Knowing how unpopular a task one is undertaking when one tries to pull out
a few more stops in that... somewhat narrow-toned organ, the modern
Englishman"
- www.phrases.org.uk [edited]
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Last Friday, New York Mayor Mamdani "pulled out all the stops" and made a pitch
to President Trump in the White House. He proposed a 12,000 housing-unit project
at the cost of $21 billion at a rail site in Queens. The idea had been floating
around for the past 20 years, some say.
