The following 3-minute blitz game is a good example of how a Jerome Gambit can just roll on.
fedronomo - Pankocurek
3 0 blitz, lichess.org, 2022
1.e4 e5 2.Nf3 Bc5 3.Bc4 Nc6 4.Bxf7+
4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ Ng6
7.Qd5+ Kf8 8.Qxc5+ Qe7 9.Qxe7+ N8xe7
White has 2 pawns in exchange for a piece. His primary actor, the Queen, has been exchanged, so he relies on the "Jerome pawns".
10.d4 Kf7 11.O-O Rf8 12.f4 Kg8
Black has castled-by-hand.
White's pawns are ready to advance.
13.f5 Nh4
"Aggressive" play, the kind of move more likely in blitz play. Still, withdrawing to h8, and then returning via f7, was a better idea.
14.Bg5 Nxg2
The right idea, to return a piece for some material. Leading to an even game would have been 14...Nhxf5 15.exf5 Nxf5.
15.Kxg2 Nc6 16.c3 d6
17.Nd2 Na5 18.Rae1 c5 19.e5 dxe5 20.dxe5 b5 21.f6 g6 22.e6
22...Bb7+ 23.Kg1 Bd5 24.e7 Rfc8 25.f7+ Bxf7 26.Ne4 Nc6 27.Nd6 Rc7
28.Rxf7 Rxe7 29.Bxe7 Nxe7 30.Rexe7
The game is won. Black's only hope is the clock.
30...Rd8 31.Rg7+ Kh8 32.Nf7+ Kxg7 33.Nxd8+ Kf6 34.Rxh7
White starts to clean up the enemy pawns, making finishing the game easier.
34...g5 35.Rxa7 g4 36.Ra5 Kf5 37.Rxb5 Kf4 38.Rxc5 Kf3 39.a4 g3 40.hxg3 Kxg3
41.a5 Kf3 42.a6 Ke2 43.a7 Kd2 44.a8=Q Kc2 45.Qg2+ Kb3 46.c4 Kb4 47.Qc6 Kb3 48.Qb5+ Kc2 49.b4 Kc3 50.Qa4 Kd4 51.Qd7+ Kc3 52.Rf5 Kxb4 53.Qb5+ Kc3 54.Rf3+ Kd4 55.Qf5 Kxc4 56.Rf4+ Kc3 57.Qh3+ Kd2 58.Rf2+ Ke1 59.Qf1 checkmate