One such Jerome Gambit "relative" was showcased in "Adolf Albin Plays the Jerome Gambit (Part 1 & 2)", highlighting the game Albin,A - Schlechter,C, Trebitsch Memorial Tournament Vienna, 1914. The game began 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Qe2 Bc5 5.Bxf7+, which easily could have been a transposition from 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Qe2 Nf6, a "modern" (no 5.Nxe5+) Jerome Gambit.
White's 4th move was anticipated at least by James Mason, who, in the August 1895 British Chess Magazine, gave a game “played recently by correspondence between Brandfort and Bloemfontein, South Africa” which went 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Qe2 d6. Mason suggested the move 4…Nf6, because “there would be plenty of time to play the Pawn - perhaps two squares instead of one. For, as the Cape Times remarks, if White adopts the ‘Jerome Gambit’ 5.Bxf7+ Black replies 5…Kxf7 6.Qc4+ d5 7.Qxc5 Nxe4 with advantage.”
The Salvio Gambit (see"The Salvio Gambit??" and "The Salvio Gambit?? [more]"), from analysis from the early 1600s, is related: 1.e4 e5 2.Bc4 Bc5 and now 3.Qe2 Nf6/Nc6 4.Bxf7+.
It is probably timely to reiterate that I refer to 1.e4 e5 2.Bc4 Bc5 3.Bxf7+ as the "Abrahams Jerome Gambit" (see "Abrahams Jerome Gambit" Part 1 & Part 2), not because Alonzo Wheeler Jerome ever played the line, nor Abrahams, as far as I know, but because it was referred to as the Jerome Gambit in The Chess Mind (1951) and The Pan Book of Chess (1965), by Gerald Abrahams.
It is hard to overlook another possible precursor: the game Hamppe - Meitner, Vienna Club, 1872, which begins a little bit like a reversed Jerome Gambit, 1.e4 e5 2.Nc3 Bc5 3.Na4 Bxf2+ and is covered in "Godfather of the Jerome Gambit? (Part I, Part II, Part III, and Endnote)".
Another opening with themes akin to the Jerome - with an initial Knight sacrifice at f7 - which may have caught Alonzo Jerome's eye - is the Sarratt Attack, 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Bc5 5.Ng5 usually followed by 5...Nh6 6.Nxf7 Nxf7 7.Bxf7+ Kxf7. Similar (although I occasionally mix them up) is the Vitzthum Attack, 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Bc5 5.Ng5 Nh6 followed by 6.Qh5. A good review can be found in the post "Capt. Evans Faces the Sarratt Attack".
Then, of course, there was the rumor that culminated in the post, here,"A GM plays the Jerome Gambit??", followed by "Here, have a Bishop..." and "Here, have another...".
That was topped by the rumor that Alexander Alekhine had defended against the Jerome Gambit - see "The Jerome Gambit is Going to Drive Me... (Part 1 & Part 2)"; and then, sadly "Much Ado About... Nothing".
Oh, oh, oh... Can we get back to the time when a modern, 2700+-rated Grandmaster didn't play the Jerome Gambit??
[to be continued]