Old story about a Company with pyramid-shaped office

Question

I'm looking for a short story, I believe by a 50s to 70s American author, about a guy who gets a coveted job at a huge Company making some unspecified products.
He gets promoted to the head office of the Company, located in a enormous pyramid-shaped skyscraper of over a hundred floors, where the higher your rank, the higher floor your office is on. The President's office is supposed to be at the apex of the pyramid.
But it's a strange company because while everyone works very hard, no-one has ever seen the President. The official line is that he is very busy. There are rumors that he is dead, or that he does not exist, and that nobody is in charge. Eventually a superior expiring on the job from overwork authorizes the protagonist to visit the company directors. He explores their offices near the top floor, which are full of the paraphernalia of their respective hobbies, but there is nobody there.
Finally he climbs to the very top tiny floor which turns out to contain the elevator motors. He finds a small window, looks out and sees that it is winter, and remembers that there is a world outside the Company.

Atom C · Accepted Answer

Update: Is it "The Top" by George Sumner Albee?
This looks more like it, thanks to comments above mentioning Groff Conklin (@user141361). I went through each of the story lists in anthologies listed in the 60s under his name on Wikipedia. Found here, I then searched for the top. From Goodreads - 12 Great Classics of Science Fiction, a comment by Chris Aldridge:

...This book contains as it's [sic] 4th story the Mindwebs audiobook 33 which is "The Top" by George Sumner Albee ... Mindwebs version from "Magazine of Fantasy and Science Fiction" 1962. A strange possibly satirical story about an advertising executives [sic] rise towards both the top position and floor, of a claustrophobic pyramidal building within a profoundly dysfunctional corporation...

Here is part of a description/review of the story, from Galactic Journey:

Career ad-man receives the promotion he’s always desired, allowing him at last to meet the President of the sprawling industrial combine of which the copywriter is just a valuable cog.  But does the Big Boss run the machine, or are they one and the same?...

I still recommend the below if you are interested in other related stories!

It doesn't fit so neatly — from the 2000s, a whole novel — but it sounds a lot like Company, by Max Barry. Here are some details that jumped out, just in case:
The titular Company is very mysterious. The CEO is a mysterious figure.

A meeting with upper management is impossible without an appointment, an appointment is impossible without the consent of mid-level managers, and managers fire anyone who ask questions outside the lines of preferred company policy.

Eventually, the protagonist is invited into a more in-the-know position.
There is a good deal of sense of character to the building, almost a character itself. Particularly regarding the floors in the building:

The description of the work taking place also seems to fit. Everyone works very hard, but few seem to really understand the work they are doing.
(Quotes: Wikipedia, Goodreads)

Old story about a Company with pyramid-shaped office

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