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The record for the most mutual checks is known, but what about the record for double checks? There are a few rules though so this question can actually have an answer.

  1. A checkmate move only counts it is a double check.

  2. Threefold repetition is in effect to avoid infinite loops. The count stops right away if it happens, although the last move still counts.

  3. The position must be legal.

I have four catergories that I have come up with. Promoted pieces allowed and not allowed are two criteria. The next two are “forced” and “unforced.” The first means that Black must allow themselves to be double-checked, and in the second they play along.

I hav done some initial work myself. Who can find more?

No Promoted Pieces, Unforced-6 Double Checks

[FEN "4K3/8/8/3p4/k1p1N3/1p4N1/P5BB/RRQ5 w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kxd5 4. Nc3+ Kd6 5. Nf5+ Kc5 6. Na4#

No Promoted Pieces, Forced-5 Double Checks

[FEN "kb1r4/P1p5/1P2P3/6NB/7B/8/8/RRQ4K w - - 0 1"]

1. axb8=Q+ Kxb8 2. bxc7+ Kc8 3. cxd8=Q+ Kxd8 4. Nf7+ Ke8 5. Nd6+ Kf8

Promoted Pieces, Unforced-9 Double Checks

[FEN "K5b1/5p2/4p3/3pR3/k1p1N1N1/1pQ5/P1B5/RR1R1RRR w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh7 8. Nf6+ Kh8 9. Nf7#

Promoted Pieces, Forced-8 Double Checks

[FEN "K4Bb1/5p2/4p3/3p4/k1p3N1/1pR5/P1B5/RQ1RRRRR w - - 0 1"]

1. axb3+ Kb5 2. bxc4+ Kc6 3. cxd5+ Kd7 4. dxe6+ Ke8 5. exf7+ Kxf8 6. fxg8=Q+ Kxg8 7. Nh6+ Kh8 8. Nf7#

Addendum:

As Hauke Reddmann noted in a comment, Ba1 Bb1 Rb2-Kc3 is a well-known double checking mechanism, but no origin is given. The earliest instance I have found, and the likely origin of it, is from 1919, which is a century ago as @Evargalo proposed a comment.

[Title "Alain Campbell White, Pittsburgh Gazette Times 4/1916 #12"]
[FEN "2q5/2pp4/3pr3/4pb2/K1p2pn1/2bn1kp1/3pr1R1/6BB w - - 0 1"]

1. Rf2+ Ke3 2. Rf3+ Ke4 3. Re3+ Kd4 4. Re4+ Kd55. Rd4+ Kc5 6. Rd5+ Kc6 7. Rc5+ Kb6 8. Rc6+ Kb7 9. Rb6+ Ka7 10. Rb7+ Ka8 11. Ra7+ Kb8 12. Ra8#

It turns out that the record for the double checks in a checkmate problem is 13 in the mainline. It cannot contend for the forced record though since Black has other options.

[Title "Стојнић, Драган Бабић, Миломир, The Problemist 2004-05, #13"]
[FEN "3q1nKB/R1P1kPRB/N3p3/1p1n2p1/2r2p2/1p2b3/P2pb2N/3r4 w - - 0 1"]

1. c8=N+ Kf6 2. Rg6+ Kf5 3. Rf6+ Ke5 4. Rf5+ Ke45. Re5+ Kd4 6. Re4+ Kd3 7. Rd4+ Kc3 8. Rd3+ Kc2 9. Rc3+ Kb2 10. Rc2+ Kb1 11. Rb2+ Ka1 12. Rb1+ Kxa2 13. Nb4#
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    Ba1 Bb1 Rb2 - Kc3 is a well known mechanism. 11 double checks. Also, the downvoters may have a point insofar as this SE is more dedicated to OTB than problem chess (still, I earned tons of undeserved upvotes by just quoting a position I happened to know from another forum, answering a problem chess question :-). That said, why don't you carry your question to the MatPlus forum, where the problem chess enthusiasts sit? They will be most interested (and also beat your records in no time :-) – Hauke Reddmann Apr 8 '19 at 7:54
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    Depending of how you handle threefold repetitions, the answer might be infinity, with W:Ka8,Ba1,Bh1,Re4 / B: Kd5 : 1.Rd4 Ke5 2.Re4 Kd5 3.Rd4 etc. – Evargalo Apr 8 '19 at 9:20
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    A (nice) problem from 2004 cannot be "the orginal problem in which [the double staircase] appears." I won't be surprised if you were off by a century ! – Evargalo Jun 5 '19 at 12:42
4

I am pretty sure I could make this last longer, but here is already a sequence with 26 unforced consecutive double-checks without promoted pieces.

[FEN "8/8/8/Rp2p3/3Pk1N1/6pB/1Q2N2B/K3R3 w - - 0 1"]

1. Nc3+ Kxd4 2. Ne2+ Ke4 3. Nc3+ Kd4 4. Ne2+ Ke4 5. Nc3+ Kd4 6. Nxb5+ Kd5 7. Nc3+ Kd4 8. Nb5+ Kd5 9. Nc3+ Kd4 10. Ne2+ Ke4 11. Nxg3+ Kf4 12. Ne2+ Ke4 13. Nc3+ Kd4 14. Nb5+ Kd5 15. Nc3+ Kd4 16. Ne2+ Ke4 17. Ng3+ Kf4 18. Ne2+ Kf5 19. Nh6+ Ke4 20. Ng3+ Kf4 21. Ne2+ Ke4 22. Nc3+ Kd4 23. Nb5+ Kd5 24. Nc3+ Kd4 25. Nb5+ Kd5 26.Nc7+

12 forced double-checks, based on the scheme given by Hauke Reddmann in a comment:

[FEN "1RN5/5p2/7p/3P3p/2P3p1/QPk4N/1R1p1K2/BB6 w - - 0 1"]

1. Rc2 Kd3 2. Rc3 Kd4 3. Rd3 Ke4 4. Rd4 Ke5 5. Re4 Kf5 6. Re5 Kf6 7. Rf5 Kg6 8. Rf6 Kg7 9. Rg6 Kh7 10. Rg7 Kh8 11. Rh7 {11. Rg8} Kg8 12.Ne7
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In the time since @Evargalo posted their answer, a new record of 14 forced double checks without promoted pieces has appeared in a selfmate problem created by Miodrag Mladenovic.

[Title "Miodrag Mladenovic, MatPlus.net Forum 14/11/2019, s#15"]
[FEN "BQN3N1/1RPRPk2/1B6/1b4np/2nr3r/4q3/4P1p1/4K3 w - - 0 1"]

1. e8=Q+ Kxe8 2. Nd6+ Kxd7 3. c8=B+ Kc6 4. Rc7+ Kxd6 5. Rc6+ Kd5 6. Rd6+ Ke5 7. Rd5+ Ke4 8. Re5+ Kf4 9. Rf5+ Kg4 10. Rf4+ Kg3 11. Rg4+ Kh3 12. Rg3+ Kh2 13. Rxg2+ Kh1 14. Rg1+ Kxg1 15. Qg3+ Qxg3#
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