A Study of DS-1103a Combination Therapy in Participants With Advanced Solid Tumors

Inclusion Criteria: * Sign and date the informed consent form (ICF), prior to the start of any study-specific qualification procedures * Adults ≥18 years of age at the time the ICF is signed (please follow local regulatory requirements if the legal age of consent for study participation is \>18 years old) * Pathologically documented HER2-expressing (immunohistochemistry \[IHC\] 1+ or greater) or HER2-mutated (activating mutation) solid tumor that is unresectable or metastatic (further detailed in inclusion criteria specific for Part 1 and Part 2 below) * Is willing and able to provide adequate baseline tumor samples. If an adequate archival tumor tissue is not available, a fresh tumor tissue biopsy is required * Presence of at least 1 measurable lesion based on computed tomography (CT) or magnetic resonance imaging (MRI) per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1) by investigator assessment * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 * Has a left ventricular ejection fraction (LVEF) ≥50% by either an echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 28 days before enrollment * Has adequate organ and bone marrow function within 28 days before the start of study treatment. Transfusion (red blood cell or platelet) or granulocyte-colony stimulating factor (G-CSF) administration is not allowed within 14 days prior to the start of study treatment. * If the participant is a female of childbearing potential, she must have a negative serum pregnancy test at Screening and must be willing to use highly effective birth control upon enrollment, during the Treatment Period, and for at least 10 months following the last dose of study drug(s). * If male, the participant must be surgically sterile or their female partner of childbearing potential must be willing to use highly effective birth control upon enrollment, during the Treatment Period, and for 6 months following the last dose of study drug(s). In addition to the above, it is recommended that the male participant uses a condom throughout this period to prevent their partner from possibly being exposed to the study drug(s) via sperm. * Male participants must not freeze or donate sperm from the time of enrollment, during the Treatment Period, and for at least 6 months after the final study drug(s) administration * Female participants must not donate, or retrieve for their own use, ova from the time of enrollment, during the Treatment Period, and for at least 10 months after the final study drug(s) administration * Is willing and able to comply with scheduled visits, drug administration plan, laboratory tests, other study procedures, and study restrictions Dose-escalation Phase: * Has progressed or was non-responsive to available therapies and for which no standard or available anticancer therapy exists * Has a pathologically documented HER2-expressing (eg, breast cancer) or HER2-mutated (eg, non-small cell lung cancer \[NSCLC\]) solid tumor (participants with gastric cancer or gastroesophageal junction adenocarcinoma are not eligible) Dose-expansion Phase: * Pathologically documented breast cancer that: * Has a history of low HER2 expression, defined as IHC 2+/in situ hybridization negative (ISH-) or IHC 1+ (ISH- or untested) according to American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) 2018 HER2 testing guidelines * Is hormone receptor (HR)-positive or HR-negative (HR-positive for estrogen receptor or progesterone receptor if finding of ≥1% of tumor cell nuclei are immunoreactive), as defined by ASCO/CAP HR testing guidelines * Has been treated with at least 1 and at most 2 prior lines of chemotherapy in the recurrent or metastatic setting. If recurrence occurred within 6 months of (neo)adjuvant chemotherapy, (neo)adjuvant therapy would count as 1 line of chemotherapy * Was never previously HER2-positive (IHC 3+ or IHC 2+/ISH+) on prior pathology testing (per ASCO/CAP guidelines) or was historically HER2 IHC 0 only * Was never previously treated with anti-HER2 therapy * Documented radiologic progression (during or after most recent treatment) Exclusion Criteria: * Has had prior treatment with an anti-CD47 or anti-signal regulatory protein α (SIRPα) therapy. * Has an inadequate treatment washout period prior to start of study treatment, defined as follows: * Major surgery: ≤4 weeks or ≤2 weeks for low-invasive cases (eg, colostomy) * Radiation therapy including palliative stereotactic radiation to chest: ≤4 weeks * Palliative stereotactic radiation therapy to other anatomic areas: ≤2 weeks * Received any systemic agent from a previous treatment regimen or clinical study within the specified time frame prior to administration of study treatment as specified in the protocol * Medical history of myocardial infarction (MI) within 6 months before study enrollment, symptomatic congestive heart failure (CHF) (New York Heart Association \[NYHA\] Class II to IV * Has a QT interval corrected with Fridericia's formula (QTcF) prolongation to \>470 ms (females) or \>450 ms (males) based on average of the screening triplicate 12-lead electrocardiogram (ECG) * Has a history of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at Screening * Has spinal cord compression or clinically active central nervous system metastases, defined as untreated and symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms * Has multiple primary malignancies within 3 years, except adequately resected non-melanoma skin cancer, curatively treated in-situ disease, other solid tumors curatively treated, or contralateral breast cancer * Has a history of severe hypersensitivity reactions to either the drug substances or inactive ingredients in the drug products or other monoclonal antibodies * Has an uncontrolled infection requiring intravenous (IV) antibiotics, antivirals, or antifungals * Is requiring concomitant use of chronic systemic (IV or oral) corticosteroids or other immunosuppressive medications during the study * Has received a live, attenuated vaccine (messenger ribonucleic acid \[mRNA\] and replication-deficient adenoviral vaccines are not considered live, attenuated vaccines) within 30 days prior to first exposure to study drug(s) * Has substance abuse or any other medical conditions such as clinically significant cardiac or psychological conditions, that may, in the opinion of the investigator, interfere with the participant's participation in the clinical study or evaluation of the clinical study results. * Has active primary immunodeficiency or active human immunodeficiency virus (HIV) infection as determined by plasma HIV ribonucleic acid (RNA) viral load and CD4 count. For the Dose-expansion phase only, participants with undetectable viral load or normalized CD4 count (CD4+ T-cell counts ≥ 350 cells/μL) and no opportunistic infection within the past 12 months will be eligible. These participants must be on established antiretroviral therapy for at least 4 weeks and have an HIV viral load \<400 copies/mL prior to enrollment. * Has active hepatitis B or C infection. Participants with past hepatitis C virus (HCV) infection and positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA. Participants with past or resolved hepatitis B virus infection are eligible only if they meet pre-specified criteria. * Has unresolved toxicities from previous anticancer therapy * Female who is pregnant, breastfeeding, or planning to become pregnant * Has lung-specific intercurrent clinically significant illnesses including, but not limited to, any underlying pulmonary disorder * Any autoimmune, connective tissue or inflammatory disorders where there is documented or a suspicion of pulmonary involvement at the time of Screening * Prior complete pneumonectomy * Any of the following within 6 months of enrollment: Cerebrovascular accident, transient ischemic attack, other arterial thromboembolic event, or pulmonary embolism * Psychological, social, familial, or geographical factors that would prevent regular follow-up * Any active or chronic corneal disorders, other active ocular conditions requiring ongoing therapy, or any clinically significant corneal disease that prevents adequate monitoring of drug-induced keratopathy * Uncontrolled hypertension (resting systolic blood pressure \>180 mmHg or diastolic blood pressure \>110 mmHg) and/or severe arrhythmia within 28 days before enrollment Dose-escalation Phase: * Same as noted above for overall study Dose-expansion Phase: * Has had prior treatment with antibody-drug conjugate that consists of an exatecan derivative that is a topoisomerase I inhibitor including prior participation in a study involving an antibody-drug conjugate