The goal of this clinical trial is to learn if the combination of lenvatinib and a PD-1 inhibitor (a type of immunotherapy) works to treat advanced solid tumors that have a specific genetic change called "11q13 amplification". It will also learn about the safety of this combination. The main questions it aims to answer are:

How many participants' tumors shrink or stop growing after receiving the combination therapy? What side effects do participants have when taking this combination therapy? All participants in this study will receive the same drug combination. Researchers will look at the results to see how well the treatment works.

Participants will:

Take lenvatinib orally once daily and receive PD-1 inhibitor by intravenous infusion every 3 weeks.

Visit the clinic regularly for checkups, blood tests, and CT or MRI scans to see how the tumor is responding.

Be followed for side effects and survival over time.

Inclusion Criteria:

• Voluntary signing of the informed consent form, age ≥ 18 years at the time of signing, any gender.
• Histologically or cytologically confirmed unresectable locally advanced or metastatic solid malignant tumor, including but not limited to: esophageal carcinoma, head and neck squamous cell carcinoma, breast cancer, lung cancer, hepatobiliary malignancies, and other solid tumors deemed eligible by the investigator.
• Confirmed tumor presence of chromosome 11q13 amplification (amplification of at least one gene among CCND1, FGF3, FGF4, FGF19) via NGS testing.
• No prior treatment with lenvatinib.
• ECOG Performance Status of 0 or 1, with an estimated life expectancy ≥ 3 months.
• At least one radiologically measurable lesion as defined by RECIST 1.1 criteria (tumor lesion with longest diameter ≥10 mm on CT scan, or lymph node with short axis ≥15 mm).
• Adequate organ function.

Exclusion Criteria:

• Presence of active or previously documented autoimmune or inflammatory disorders.
• Known hypersensitivity to any component of the study drugs (lenvatinib or PD-1 inhibitors).
• Significant bleeding tendency or coagulation dysfunction, or occurrence of major bleeding within 4 weeks prior to enrollment.
• Uncontrolled hypertension (systolic blood pressure ≥140 mmHg or diastolic blood pressure ≥90 mmHg) despite medication.
• Received chemotherapy, radiotherapy, major surgery, or other anticancer therapy within 4 weeks prior to enrollment.
• Pregnant or lactating women, or patients of childbearing potential unwilling to use effective contraception.
• Inability to comply with the study protocol for treatment or scheduled follow-up assessments.