This study utilizes large-scale shell model calculations with the extended pairing and multipole–multipole force model (EPQQM) to investigate low-lying states in the nuclei of 42Ca, 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2Sc, and 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2Ti. The model space in this study includes the fp shell as well as the intruder 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2 orbit, which accurately reproduces the positive parity levels observed in the aforementioned nuclei and predicts high energy states with negative parity coupled with the intruder 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2. The study further predicts two different configurations in 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2Ti at around 6 MeV, specifically 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2 and 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2, both of which involve the intruder orbit 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2. The levels coupled with the intruder 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2 in 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2Ti are predicted to lie between 7 and 11 MeV. The inclusion of the intruder orbit 4242-44g9/2g9/243πf7/22νg9/2πf7/2g9/2νf7/2g9/2g9/244g9/2 is crucial for the exploration of high energy states in the northeast region of the doubly magic nucleus 40Ca.