A Study of DS-3939a in Participants With Solid Tumors

Inclusion Criteria:

1. Sign and date the Main Trial informed consent form (ICF), prior to the start of any trial-specific procedures.
2. Adults greater than or equal to (≥)18 years of age at the time the Main Trial ICF is signed (follow local regulatory requirements if the legal age of consent for trial participation is \>18 years old).
3. Histologically documented Stage IIIB, IIIC disease who is not candidate for surgical resection or definitive chemoradiation, or Stage IV NSQ NSCLC.
4. Has a left ventricular ejection fraction (LVEF) ≥50 percent (%) by either an echocardiogram (ECHO) or multigated acquisition scan (MUGA) within 28 days of the first trial intervention.
5. Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 assessed no more than 14 days prior to initiation of trial interventions.
6. Has adequate organ function.
7. Participants must have measurable disease by investigator assessment according to RECIST v1.1.

Additional Inclusion Criteria for Substudy 1:

1\. Participants must not have received prior systemic therapy for locally advanced unresectable or metastatic NSCLC.

Additional Inclusion Criteria for Substudy 2:

1. Participants with AGA (excluding EGFR mutation): Participants have been previously treated with targeted therapy for the AGA and platinum-based chemotherapy for the advanced disease setting.
2. Participants without AGA: Participants have been previously treated with platinum-based chemotherapy and anti-programmed death-1 (anti-PD-1)/programmed death-ligand 1 (PD-L1) antibody
3. Part 2 only: Participants must have received only 1 or 2 prior lines of anticancer therapy for the advanced disease setting.

Exclusion Criteria:

1. Prior systemic anticancer therapy targeting MUC1 or TA-MUC1.
2. Prior systemic anticancer therapy with topoisomerase 1 inhibitor or topoisomerase 1 inhibitor-based antibody-drug conjugate (ADCs) (e.g., datopotamab deruxtexan and Sacituzumab govitecan).
3. Has spinal cord compression or clinically active central nervous system (CNS) metastases.
4. Has multiple primary malignancies.
5. Has any history of interstitial lung disease (ILD)/pneumonitis irrespective of steroid use, or current ILD, or suspected ILD, or ILD that cannot be ruled out by imaging at screening
6. Has active or uncontrolled human immunodeficiency virus (HIV) infection.
7. Has active or uncontrolled hepatitis B virus (HBV)/hepatitis C virus (HCV) infection.
8. Any of the following within the past 6 months: cerebrovascular accident, transient ischemic attack, or other arterial thromboembolic event.
9. Current participation in other therapeutic investigational procedures, except for participation in long term survival follow-up (LTSFU) without any investigational treatment.