Most chess sets come with only one spare queen, and according to the video in the question Is holding the opponent's captured pieces legal or allowed?, one cannot use an upside down rook, and doing so it results in promotion to a rook.

If two queens already on the board, how can one promote a third one?

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    I wish most chess sets came with one spare queen Dec 12 '20 at 22:00
  • @MichaelWest, I meant tournament set, and I think all USCF tournament sets come with one spare queen.
    – Akavall
    Dec 12 '20 at 23:24
  • Good answers below. They apply to underpromotions too. Dec 13 '20 at 13:52
  • I don't think I've ever seen a single chess set with extra pieces. I've never sought out an "official tournament" grade chess set, but are those even a thing? Dec 14 '20 at 19:52
  • @MichaelRichardson, Yes, for example: chessusa.com/product/…
    – Akavall
    Dec 14 '20 at 19:56

Under USCF rule 8F7:, it is acceptable to place a rook upside-down if a spare queen is not available.

If the desired piece is not available to replace a promoted pawn, the player may stop both clocks in order to locate that piece and place it on the board. A player who cannot quickly find such a piece may request the assistance of the director. It is common practice, however, to play using an upside-down rook for a second queen. In the absence of the player’s announcement to the contrary, an upside-down rook shall be considered a queen.

Under FIDE rules, you can't use an upside-down rook as a spare queen, but you can find the answer hidden in the section about the clocks:

6.11.2 A player may stop the chessclock only in order to seek the arbiter’s assistance, for example when promotion has taken place and the piece required is not available.

  • "Under FIDE rules, you can't do that" - can't do what?
    – Pedro A
    Dec 14 '20 at 4:21
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    @PedroA : This post has two sentences, both describing the same activity: "plac[ing] a rook upside-down if a spare queen is not available". Dec 14 '20 at 4:43
  • 3
    @PedroA I had the same trouble reading this answer. The first sentence answers the broad question. Everything else is commenting on a quote taken from O.P.'s question, regarding the rules to stop the clock. Dec 14 '20 at 14:36
  • I edited that part since people were finding it confusing.
    – D M
    Dec 14 '20 at 21:48

You pause the clock, call an arbiter and an additional queen will be provided.

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