A Study of Patritumab Deruxtecan in Pediatric Participants With Relapsed or Refractory Solid Tumors (MK-9999-01C/LIGHTBEAM-U01)

Researchers are looking for new ways to treat children with hepatoblastoma or rhabdomyosarcoma (RMS) that has relapsed or is refractory: * Hepatoblastoma is a common liver cancer in babies and very young children * RMS is a cancer that starts in muscle cells, often in a child's head and neck, bladder, arms, or legs * Relapsed means the cancer came back after treatment * Refractory means the cancer did not respond (get smaller or go away) to treatment The study treatment HER3-DXd (also known as MK-1022 or patritumab deruxtecan) is an antibody-drug conjugate (ADC). An ADC attaches to a protein on cancer cells and delivers treatment to destroy those cells. The goals of this study are to learn: * About the safety of HER3-DXd in children and if they tolerate it * What happens to HER3-DXd in children's bodies over time * If children who receive HER3-DXd have the cancer get smaller or go away

This study will have 2 parts: a safety lead-in to demonstrate a tolerable safety profile and confirm a preliminary recommended phase 2 dose (RP2D) (Part 1) followed by an efficacy evaluation (Part 2)

The main inclusion criteria include but are not limited to the following: * Has one of the following histologically confirmed advanced or metastatic solid tumors: Rhabdomyosarcoma (RMS), or Hepatoblastoma * Has progressed after at least 1 prior systemic treatment for RMS or hepatoblastoma and who has no satisfactory alternative treatment option (ie, is ineligible for other standard treatment regimens) * Participants who have adverse events (AEs) due to previous anticancer therapies must have recovered to Grade ≤1 or baseline. Participants with endocrine-related AEs who are adequately treated with hormone replacement or participants who have Grade ≤2 neuropathy are eligible. Participants with Grade ≤2 alopecia are also eligible * Hepatitis B surface antigen (HBsAg) positive participants are eligible if they have received hepatitis B virus (HBV) antiviral therapy and have undetectable HBV viral load * Participants with a history of hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable The main exclusion criteria include but are not limited to the following: * Has a history of (noninfectious) interstitial lung disease (ILD)/pneumonitis that required steroids or has current ILD/pneumonitis, and/or suspected ILD/pneumonitis that cannot be ruled out by standard diagnostic assessments * Has clinically severe respiratory compromise resulting from intercurrent pulmonary illness * Has a history of solid organ transplant * Has a history of allogeneic stem cell transplant * Has clinically significant corneal disease * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis/leptomeningeal disease; participants with previously treated brain metastases may participate provided they are radiologically stable (ie, without evidence of progression) for at least 4 weeks * Has uncontrolled or significant cardiovascular disorder * Has a history of clinically significant congenital cardiac syndrome * Has a history of human immunodeficiency virus (HIV) infection * Has a known additional malignancy that is progressing or has required active treatment within the past 1 year * Has an active infection requiring systemic therapy * Has concurrent active hepatitis B (HBsAg positive and/or detectable HBV deoxyribonucleic acid \[DNA\]) and HCV defined as anti-HCV antibody (Ab) positive and detectable HCV ribonucleic acid \[RNA\]) infection * Has not adequately recovered from major surgery or have ongoing surgical complications