MK-7684A With or Without Other Anticancer Therapies in Participants With Selected Solid Tumors (MK-7684A-005) (KEYVIBE-005)

Inclusion Criteria:

* One of the following histologically or cytologically confirmed, advanced (unresectable or metastatic) solid tumors:

  * Squamous cell carcinoma, adenosquamous carcinoma, or adenocarcinoma of the cervix
  * Endometrial cancer
  * Head and neck squamous cell carcinoma (HNSCC)
  * Unresectable biliary adenocarcinoma (gallbladder or biliary tree \[intrahepatic or extrahepatic\] cholangiocarcinoma)
  * Adenocarcinoma or squamous cell carcinoma of the esophagus or advanced/metastatic Siewert type 1 adenocarcinoma of the gastroesophageal junction (GEJ).
  * Triple-negative breast cancer (TNBC)
  * Hepatocellular carcinoma (HCC)
  * Urothelial carcinoma of the renal pelvis, ureter, bladder, or urethra
  * Ovarian cancer
  * Gastric cancer
* Measurable disease per RECIST v1.1 as assessed by BICR or local site investigator.
* Adequately controlled blood pressure (BP) with or without antihypertensive medications.
* Human immunodeficiency virus (HIV)-infected participants must have well controlled HIV on anti-retroviral therapy (ART).
* Male participants must agree to follow contraceptive guidance.
* Female participants are not pregnant or breastfeeding, not a woman of child-bearing potential (WOCBP) or is a WOCBP and agrees to follow contraceptive guidance.
* Adequate organ function.

Exclusion Criteria:

* History of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 3 years.
* Prior therapy with anti-programmed cell-death (PD-1), anti-PD-L1, anti-PD-L2, or anti-T-cell immunoreceptor with Ig and ITIM domains (TIGIT) agent.
* Prior systemic anticancer therapy including investigational agents within 4 weeks before randomization/allocation.
* Received a live or live-attenuated vaccine within 30 days before the first dose of study intervention. Administration of killed vaccines are allowed.
* Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days before the first dose of study medication.
* Active autoimmune disease that has required systemic treatment in past 2 years.
* Active infection requiring systemic therapy.
* Concurrent active hepatitis B and hepatitis C virus infection.
* History of allogenic tissue/solid organ transplant.
* Previous treatment with lenvatinib (for participants who will receive lenvatinib in their assigned treatment arm).
* Has clinically significant cardiovascular disease within 12 months from first dose of study intervention.