Testing the Safety of the Combination of Anti-Cancer Drugs CX-5461 (Pidnarulex) and Trastuzumab Deruxtecan (T-DXd) for Human Epidermal Growth Factor Receptor 2 (HER2)-Positive Solid Tumors and Breast Cancer

Patients with a history of (non-infectious) interstitial lung disease (ILD) that required steroids, have current ILD, or where there is suspected ILD that cannot be ruled out by imaging at screening. These patients will be excluded because T-DXd is known to increase the risk of developing ILD and pneumonitis

Patients with clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses including, but not limited to, any underlying pulmonary disorder (i.e., pulmonary emboli within three months of the study enrollment, severe asthma, severe chronic obstructive pulmonary disease [COPD], restrictive lung disease, pleural effusion, etc.), and any autoimmune, connective tissue or inflammatory disorders with potential pulmonary involvement (i.e., Rheumatoid arthritis, Sjogren's, sarcoidosis, etc.), or prior pneumonectomy at the time of screening. These patients will be excluded because T-DXd is known to increase the risk of developing ILD and pneumonitis

Patients who have had chemotherapy (including antibody drug therapy, retinoid therapy, hormonal therapy for cancer) within 3 weeks (2 weeks or five half-lives, whichever is longer for small-molecule targeted agents such as 5-fluorouracil-based agents, folinate agents), weekly paclitaxel; 6 weeks for nitrosoureas or mitomycin C. These patients will be excluded to allow for recovery of toxicities related to chemotherapy and minimize risk of drug interactions

Patients who have had cancer immunotherapy including monoclonal antibody therapy within 4 weeks