Breast cancer begins in the breast cells, mainly impacting women. It starts in the cells that line the milk ducts or lobules responsible for producing milk and can spread to nearby tissues and other body parts. In 2020, around 2.3 million women across the globe received a diagnosis, with an estimated 685,000 deaths. Additionally, 7.8 million women were living with breast cancer, making it the fifth leading cause of cancer-related deaths among women. The mutational changes, overexpression of drug efflux pumps, activation of alternative signalling pathways, tumour microenvironment, and cancer stem cells are causing higher levels of drug resistance, and one of the major solutions is to identify multitargeted drugs. In our research, we conducted a comprehensive screening using HTVS, SP, and XP, followed by an MM/GBSA computation of human-approved drugs targeting HER2/neu, BRCA1, PIK3CA, and ESR1. Our analysis pinpointed IRESSA (Gefitinib-DB00317) as a multitargeted inhibitor for these proteins, revealing docking scores ranging from −4.527 to −8.809 Kcal/mol and MM/GBSA scores between −49.09 and −61.74 Kcal/mol. We selected interacting residues as fingerprints, pinpointing 8LEU, 6VAL, 6LYS, 6ASN, 5ILE, and 5GLU as the most prevalent in interactions. Subsequently, we analysed the ADMET properties and compared them with the standard values of QikProp. We extended our study for DFT computations with Jaguar and plotted the electrostatic potential, HOMO and LUMO regions, and electron density, followed by a molecular dynamics simulation for 100 ns in water, showing an utterly stable performance, making it a suitable drug candidate. IRESSA is FDA-approved for lung cancer, which shares some pathways with breast cancers, clearing the hurdles of multitargeted drugs against breast and lung cancer. This has the potential to be groundbreaking; however, more studies are needed to concreate IRESSA’s role.