Dose Escalation Trial of BNT152+153 in Patients With Cancer

Inclusion Criteria: * Histologically or cytologically confirmed solid tumor that is metastatic (Stage IV) or unresectable and for whom there is no available standard therapy likely to confer clinical benefit, or patient who is not a candidate for such available therapy. If there is no contraindication, patients should have exhausted all standard of care therapies before entering the trial. * Measurable disease per RECIST1.1. * Male and female aged ≥ 18 years. * Prior to any trial-related assessments or procedures, must sign an informed consent form (ICF) indicating that he or she understands the purpose and procedures required for the trial and are willing to participate in the trial. * Eastern Cooperative Oncology Group performance status of 0 to 1. * Adequate coagulation function at screening as determined by: 1. International normalized ratio or prothrombin time ≤ 1.5 × upper limit normal (ULN); unless on therapeutic anticoagulants with values within therapeutic window), 2. Activated partial thromboplastin time ≤ 1.5 × ULN (unless on therapeutic anticoagulants with values within therapeutic window). * Adequate hematologic function at screening as determined by: 1. White blood cell count (WBC) ≥ 3 × 10\^9/L 2. Absolute neutrophil count ≥ 1.5 × 10\^9/L (patient may not use granulocyte-colony stimulating factor or granulocyte-macrophage colony stimulating factor to achieve these WBC and absolute neutrophil count levels) 3. Platelet count ≥ 100 × 10\^9/L 4. Hemoglobin ≥ 9.0 g/dL * Adequate hepatic function at screening as determined by: 1. Total bilirubin ≤ 1.5 mg/dL (or ≤ 2.0 mg/dL for patients with known Gilbert's syndrome or liver metastasis) 2. Aspartate aminotransferase and alanine aminotransferase ≤ 2.5 × ULN; ≤ 3 × ULN for patients with liver metastasis. 3. Albumin range ≥30 g/L * Adequate renal function at screening as determined by: Glomerular filtration rate (GFR) ≥ 45 mL/min/1.73 m\^2 - according to the Chronic Kidney Disease Epidemiology Collaboration equation, expressed as a single equation: GFR = 141 × min(Scr/κ,1)\^α × max(Scr/κ, 1)\^-1.209 × 0.993\^Age × 1.018 \[if female\] × 1.159 \[if black\]; Scr is serum creatinine (mg/dL), κ is 0.7 for females and 0.9 for males, α is -0.329 for females and -0.411 for males, min indicates the minimum of Scr/κ or 1, and max indicates the maximum of Scr/κ or 1. For creatinine assays using methods traceable to isotope dilution mass spectrometry assigned National Institute of Standards and Technology certified reference materials (Levey et al. 2009). * Able and willing to comply with scheduled visits, treatment schedule, laboratory tests, lifestyle restrictions, and other requirements of the trial. * Women of childbearing potential (WOCBP) must have a negative serum (beta-human chorionic gonadotropin) test/value at screening. Patients who are post-menopausal or permanently sterilized can be considered as not having reproductive potential. * WOCBP must agree to use highly effective contraception during the trial and for 6 months after receiving the last dose of BNT152 or BNT153. Birth control methods are considered highly effective if they have a failure rate of less than 1% per year, when used consistently and correctly. * WOCBP must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the entire trial, until 6 months after last BNT152 or BNT153 treatment. * A man who is sexually active with a WOCBP and has not had a vasectomy must agree to use a barrier method of birth control, e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also agree to not donate sperm during the trial and for 6 months after receiving the last dose of BNT152 or BNT153. * For enrollment into the biomarker cohort only: The biomarker cohort will be conducted at selected sites only. At enrollment patients must have at least one lesion that is deemed accessible by the investigator which is different from the target lesion. Also, patients must agree to have one pre-dose biopsy (baseline) and at least one on-treatment biopsy (preferred C2D8) from the same tumor lesion. Exclusion Criteria: Prior and concomitant therapy: * Use of any investigational medical product or device within 28 days before administration of first dose of trial treatment. * Has been receiving: radiotherapy, chemotherapy, or molecularly-targeted agents or tyrosine kinase inhibitors within 2 weeks or 5 half-lives (whichever is longer) of the start of trial treatment; immunotherapy/monoclonal antibodies for systemic anticancer treatment within 3 weeks of the start of trial treatment; nitrosourea, antibody-drug conjugates, or radioactive isotopes within 6 weeks of the start of trial treatment. * Ongoing participation in the active treatment phase of an interventional clinical trial. * Receives concurrent systemic (oral or intravenous) steroid therapy \>10 mg prednisone daily or its physiological equivalent for an underlying condition. * Has had major surgery within the 4 weeks before the first dose of trial treatment. * Ongoing or active infection requiring intravenous treatment with anti-infective therapy that has been administered less than 2 weeks prior to the first dose of trial treatment. * Has side effects of any prior therapy or procedures for any medical condition not recovered to NCI CTCAE v.5 Grade ≤ 1. Note: peripheral neuropathy Grade ≤ 2 is allowed; alopecia of any grade is allowed. Medical conditions: * Current evidence of new or growing brain or leptomeningeal metastases during screening. Patients with known brain metastases may be eligible if they: 1. had radiotherapy, surgery or stereotactic surgery for the brain metastases, 2. have no neurological symptoms (excluding Grade ≤ 2 neuropathy), 3. have stable brain metastasis on the computerized tomography (CT) or magnetic resonance imaging (MRI) scan within 4 weeks before signing the informed consent, 4. are not undergoing acute corticosteroid therapy or steroid taper. Notes: Patients with central nervous system symptoms should undergo a CT-scan or MRI of the brain to exclude new or progressive brain metastases. Spinal bone metastases are allowed, unless imminent fracture with cord compression is anticipated. * Has a history of a cerebrovascular accident or had a transient ischemic attack less than 6 months before signing the ICF. * Effusions (pleural, pericardial, or ascites) requiring drainage. * Active autoimmune disease including but not limited to inflammatory bowel disease, systemic lupus erythematosus, ankylosing spondylitis, scleroderma, or multiple sclerosis (except type 1 diabetes with well-regulated blood sugar). * Has any active immunologic disorder or after organ transplantation requiring immunosuppression with steroids or other immunosuppressive agents (e.g., azathioprine, cyclosporine A) with the exception of patients with isolated vitiligo, resolved childhood asthma or atopic dermatitis, controlled hypoadrenalism or hypopituitarism, and patients with a history of Graves' disease with stable thyroid function. Patients with controlled hyperthyroidism must be negative for thyroglobulin, thyroid peroxidase antibodies, and thyroid stimulating immunoglobulin prior to administration of trial treatment. * Known history of seropositivity for human immunodeficiency virus (HIV) with cluster of differentiation (CD) 4+ T-cell (CD4+) counts \<350 cells/µL and with a history of acquired immunodeficiency syndrome-defining opportunistic infections. * Known history/positive serology for hepatitis B requiring active antiviral therapy (unless immune due to vaccination or resolved natural infection or unless passive immunization due to immunoglobulin therapy). Patients with positive serology must have hepatitis B virus viral load below the limit of quantification. * Active hepatitis C virus infection; patients who have completed curative antiviral treatment with hepatitis C virus viral load below the limit of quantification are allowed. * Notes: Country-specific criterion for Czech Republic: To confirm that a patient would be eligible, an active infection with HIV/Hepatitis B or C should be ruled out by serum blood test at screening. * Known hypersensitivity to a component of any trial treatment. * Another primary malignancy that has not been in remission for at least 2 years, with the exception of those with a negligible risk of metastasis or death (including but not limited to adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer, or ductal carcinoma in situ). In case of uncertainties, the medical monitor should be consulted. Other comorbidities: * Abnormal electrocardiograms that are clinically significant, such as Fridericia-corrected QT prolongation \>480 ms. * In the opinion of the treating investigator, has any concurrent conditions that could pose an undue medical hazard or interfere with the interpretation of the trial results; these conditions include, but are not limited to: 1. Ongoing or active infection requiring antibiotic/antiviral/antifungal therapy. 2. Concurrent congestive heart failure (New York Heart Association Functional Classification Class III or IV). 3. Concurrent unstable angina. 4. Known medical history of cardiac arrhythmia (including asymptomatic atrial fibrillation). 5. Acute coronary syndrome within the previous 6 months. 6. Symptomatic pulmonary embolism within the previous 3 months. 7. Significant pulmonary disease (shortness of breath at rest or on mild exertion) for example due concurrent severe obstructive pulmonary disease. * Cognitive, psychological or psychosocial impediment that would impair the ability of the patient to receive therapy according to the protocol or adversely affect the ability of the patient to comply with the informed consent process, protocol, or protocol-required visits and procedures. * Is pregnant or breastfeeding. * Patients unable to consent. * Use of any live vaccines from 30 days prior to administration of first dose of trial treatment, during the trial, and 90 days after administration of last dose of trial treatment.