A Study to Evaluate the Safety and Efficacy of Gocatamig (MK-6070) and Ifinatamab Deruxtecan (I-DXd) in Participants With Relapsed/Refractory Extensive-Stage Small Cell Lung Cancer (MK-6070-002)

Researchers are looking for new ways to treat people with extensive-stage small cell lung cancer (SCLC) that has relapsed or is refractory. Gocatamig is a new type of immunotherapy that uses a person's immune system to find and destroy cancer cells. Ifinatamab deruxtecan (also known as I-DXd) is a drug which binds to a specific target on cancer cells and delivers treatment to destroy those cells. Researchers want to know if giving gocatamig and/or I-DXd can treat SCLC that did not respond or stopped responding to a prior treatment.

The goals of this study are to learn:

* If gocatamig and I-DXd are safe and well tolerated
* If people who receive gocatamig and I-DXd have their SCLC get smaller or go away

This study will consist of two parts. Part 1 will assess the safety, tolerability, and efficacy of gocatamig and I-DXd at dosing intervals of once every 2 weeks (Q2W) and/or once every 3 weeks (Q3W) at doses determined in study MK-6070-001 (NCT: NCT04471727). Part 2 will assess the safety and tolerability of gocatamig in Japanese participants.

Eligibility Criteria:
Inclusion Criteria:

* Has histologically or cytologically confirmed SCLC that is extensive stage (defined as Stage IV (T any, N any, M1a/b/c) following at least 1 prior line of systemic therapy that included platinum-based chemotherapy
* Must be able to provide archival tissue sample or fresh biopsy tissue sample
* Human immunodeficiency virus (HIV) infected participants must have well controlled HIV on antiretroviral therapy (ART)

Exclusion Criteria:

* Pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedure
* History of (noninfectious) pneumonitis/interstitial lung disease (ILD) that required steroids or has current pneumonitis/ILD, and or suspected ILD/pneumonitis
* Has clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses
* History of clinically significant intracranial bleeding or spinal cord bleeding
* Active neurologic paraneoplastic syndrome
* Active or history of immune deficiency with the exception of HIV-infected participants with well controlled HIV on ART
* History within 6 months before the first dose of study intervention of coronary/peripheral artery bypass graft and/or any coronary/peripheral angioplasty or clinically significant cardiovascular disease such as myocardial infarction, symptomatic congestive heart failure (CHF) (New York Heart Association \> class II), and/or uncontrolled cardiac arrhythmia
* Has other uncontrolled or significant protocol-specified cardiovascular disease
* History of arterial thrombosis (eg, stroke or transient ischemic attack) within 6 months before the first dose of study intervention
* Chronic liver disease, including liver cirrhosis of Child-Pugh class B or C
* Active clinically significant infection requiring systemic therapy
* History of allogeneic tissue/solid organ transplant
* History of leptomeningeal disease
* Received prior radiotherapy within 2 weeks of start of study intervention, or has radiation-related toxicities, requiring corticosteroids
* Ongoing treatment with immunosuppressive medications, with protocol-specified exceptions
* Known additional malignancy that is progressing or has required active treatment within the past 3 years
* Untreated or symptomatic brain metastases
* Active viral hepatitis, defined as hepatitis A (hepatitis A virus immunoglobulin M \[IgM\] positive in the setting of associated signs/symptoms), hepatitis B (hepatitis B virus surface antigen \[HbsAg\] positive and/or detectable hepatitis B virus (HBV) deoxyribonucleic acid \[DNA\]), or hepatitis C (hepatitis C virus \[HCV\] antibody positive and detectable HCV ribonucleic acid). Participants with HBV with undetectable viral load after treatment are eligible. Participants with HCV with undetectable virus after treatment are eligible.
* Part 1 only: Radiation therapy to the lung \>30 Gy within 6 months before the start of study intervention
* Part 1 only: Abdominal radiation within 4 weeks before start of study intervention
* Part 1 only: Other anticancer therapy, including cytotoxic agents, targeted agents, immunotherapies, antibody, retinoid, transplant, or anticancer hormonal treatment (except luteinizing hormone-releasing hormone \[LHRH\]) within 2 weeks before start of study intervention
* Part 1 only: Antibody-based cancer therapy within 3 weeks before start of study intervention
* Part 1 only: Chloroquine/hydroxychloroquine within 2 weeks before start of study intervention
* Part 1 only: Clinically significant corneal disease