Key Inclusion Criteria (applicable to all participants and all parts unless otherwise specified):
* Aged ≥18 years at the time of giving informed consent. Local laws will be followed if the age of consent is older.
* Have histologic or cytologic documented advanced disease, either at relapse or upon diagnosis of metastatic disease. This requirement may be considered met when advanced disease derives from unequivocal progression of a previously biopsied site of disease (e.g., progression of residual tumor after concomitant chemo-radiation for Stage III NSCLC).
* Have measurable disease defined by RECIST v1.1.
* All participants must provide a tumor tissue sample (Formalin-fixed paraffin-embedded \[FFPE\] slides) from archival tissue. The archival tissue can be an FFPE block or freshly cut slides derived from the advanced setting or a new/fresh tumor biopsy.
* Have ECOG performance status of 0 or 1.
* Have adequate organ and bone marrow function (as specified in the protocol) within 7 days before randomization/enrollment.
* Cohort 1A:
* Have histologically or cytologically confirmed diagnosis of unresectable or metastatic cutaneous melanoma not amenable to local therapy.
* Participants must have previously received a PD-1 or PD-L1 inhibitor, and, for participants with human gene that encodes a protein called B-Raf (BRAF) gene mutant melanoma, a prior treatment regimen that included vemurafenib, dabrafenib, or another BRAF gene inhibitor with or without mitogen-activated protein kinase protein inhibitor, if available and clinically indicated per local standard of care (SoC) and have experienced progression during or after the previous treatment or discontinued from prior therapy due to intolerance.
* Cohort 1B and 1C: Have advanced (i.e., metastatic or locally recurrent where local therapy with curative intent is not possible) non-squamous or squamous NSCLC.
* Cohort 1B:
* Have no actionable genomic alterations, such as EGFR mutations, anaplastic lymphoma kinase rearrangements, or other genomic alterations for which targeted molecular therapies are available. For enrolled participants with predominantly squamous histology tumors, molecular testing will not be required in cases where it is not part of the SoC.
* Have experienced relapse or progression during or after treatment with standard systemic therapy including platinum-based chemotherapy and/or immune checkpoint inhibitor in the advanced/metastatic setting or discontinued from prior therapy due to intolerance.
* Participants must have received 1 to 3 lines of systemic treatment, which can include anti-PD-1/PD-L1 therapy (if PD-L1 positive), chemotherapy, and anti-angiogenic agents. These treatments may be administered concurrently or sequentially. Prior chemotherapy must be limited to 2 lines or less.
* Cohort 1C:
* Have documented positive test results for an EGFR-sensitizing mutation (EGFR-sensitizing mutation Exon 21-L858R and 19del).
* Participants must have received one or two prior lines of systemic therapy for advanced and/or metastatic disease, which must include treatment with an approved EGFR Tyrosine Kinase Inhibitors (TKI), with at least one being a third-generation EGFR TKI. If there is no third-generation EGFR TKI approved as part of SoC by local health authorities in a certain country, failure/progression on any EGFR TKI is acceptable for eligibility.
* Participants receiving an EGFR TKI at the time of signing informed consent may continue to take the EGFR TKI until 5 days prior to Cycle 1 Day 1.
* Prior chemotherapy and amivantamab are permitted only if administered in combination with an EGFR TKI as part of a single line of therapy and as the initial (first line) treatment for advanced/metastatic disease. Participants must not have received any other systemic therapies (such as chemotherapy, immunotherapy, or targeted agents) for advanced/metastatic disease, unless those treatments were given in combination with an EGFR TKI.
* Have experienced progression during or after treatment or discontinued from prior therapy due to intolerance.
* Cohort 1D:
* Have histologically or cytologically confirmed diagnosis of unresectable or metastatic acral/uveal/mucosal melanoma not amenable to local therapy.
* Participants must have:
* Previously been treated with a PD-1 or PD-L1 inhibitor, if clinically indicated and available per local SoC, and/or
* For participants with Human Leukocyte Antigen Alleles (HLA-A)\*02:01 serotype-positive disease (only applicable for uveal melanoma), previously been treated with tebentafusp-tebn if clinically indicated and available per local SoC, and
* Experienced progression during or after the previous treatment or discontinued from prior therapy due to intolerance.
* Cohorts 1E and 1F (DDI):
* Have histologically or cytologically confirmed diagnosis of unresectable or metastatic advanced solid tumor not amenable to ablative or curative approach including, but not limited to:
* Cholangiocarcinoma, including tumors of the intra- and extrahepatic biliary tract and gallbladder
* Hepatocellular carcinoma (HCC).
* Renal cell carcinoma
* Endometrial carcinoma, excluding those classified as true sarcomas
* Pancreatic ductal adenocarcinoma (PDAC) (see below other related inclusion criterion)
* Neuroendocrine tumor of pancreatic, gastrointestinal, lung, and thymus that is well differentiated, Grade 1 to 3.
* NSCLC (Cohort 1F only)
* Have experienced disease progression on at least one and no more than three lines of prior therapy or, for Cohort 1E only, discontinued from prior therapy due to intolerance.
* (For participants with PDAC only) Have received one or two lines of systemic therapy for metastatic tumors, and have experienced progression or intolerance to the treatment during or following therapy.
* Cohort 2A: Have histologically or cytologically confirmed diagnosis of unresectable or metastatic cutaneous melanoma not amenable to local therapy.
* Cohort 2B: Have histologically or cytologically confirmed diagnosis of recurrent unresectable or metastatic breast cancer that is documented as HER2-negative and either HR-negative or HR-positive per American Society of Clinical Oncology/College of American Pathologists guidelines.
* Cohort 2D:
* Histologically and/or cytologically documented metastatic adenocarcinoma and squamous carcinoma of GC/GEJC. (Note: ESCC is excluded).
* (2L subgroup): Had disease progression during or after one prior line of anti-cancer therapy for recurrent/metastatic disease.
* (3L subgroup): Has received two or more lines of prior anti-cancer therapy for recurrent/metastatic disease.
* (HER2-expression positive subgroup): Has received at least one prior line of systemic therapy for recurrent or metastatic disease, including a HER2-targeted agent in accordance with local SoC.
* Cohort 2E:
* Histologically and/or cytologically documented recurrent unresectable metastatic colorectal adenocarcinoma.
* Must have received at least one line to a maximum of three lines of prior SoC treatment for recurrent/metastatic disease.
* Cohort 1G and 2F:
* Histologically and/or cytologically documented recurrent unresectable metastatic cervical cancer with squamous cell, adenocarcinoma, or adenosquamous histology.
* Must have received platinum-based chemotherapy, with or without an anti-PD-(L)1 agent and bevacizumab for metastatic/recurrent disease, unless the patient is not a candidate in the opinion of the treating physician.
Key Exclusion Criteria (applicable to all participants and all parts unless otherwise specified):
* Have a history of intolerance to treatment with a topoisomerase I inhibitor or intolerance to an ADC that consists of a topoisomerase I inhibitor, including but not limited to topotecan, irinotecan, and deruxtecan (e.g., severe diarrhea).
* Have an uncontrolled concomitant or intercurrent illness that contra-indicates study participation, limits compliance with study procedures or substantially increases the risk of incurring adverse events, including:
* Bleeding diathesis or active hemorrhage,
* Active infection,
* Child-Pugh class B or C cirrhosis,
* Pulmonary disease with significant impact in lung function
* Oncologic emergencies or complications (e.g., malignant hypercalcemia, superior vena cava syndrome, carcinoid syndrome that is unstable and with available alternative therapies),
* Psychiatric or abuse condition
* Infectious colitis Grade ≥2 not resolved to Grade 1 within 72 hours within the past 3 months.
* Have LVEF \<50% by either echocardiography or multi-gated acquisition (scanning) within 28 days before randomization/enrollment.
* Have clinically uncontrolled pleural effusion, ascites or pericardial effusion requiring drainage, peritoneal shunt, or cell-free concentrated ascites reinfusion therapy within 2 weeks prior to randomization/enrollment.
* Have a history of (non-infectious) interstitial lung disease (ILD) /pneumonitis that required steroids, have current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. Asymptomatic interstitial changes caused by previous radiation therapy, chemotherapy, or other factors such as smoking are acceptable.
* Are a participant of child-bearing potential who are pregnant or breastfeeding or are planning pregnancy within 225 days (\~7.5 months) after receiving last dose of BNT326 and within 6 months after last dose of BNT327, whichever is longer.
* Are potentially fertile males, who are planning to father children during the study or within 135 days (\~4.5 months) after the last dose of BNT326 and within 6 months after last dose of BNT327, whichever is longer.
* Are subject to exclusion periods from another investigational study.
* Specific to BNT327: Participants with significant risks of hemorrhage or evidence of major coagulation disorders as specified in the protocol.
* Specific to BNT327: Have a history of intolerance to treatment with an anti-VEFG, anti-PD-1/PDL-1, or similar substance, including, but not limited to, bevacizumab, ramucirumab, atezolizumab, pembrolizumab, nivolumab, or other related therapies.
* Cohort 1E: Have histological diagnosis of fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC.
NOTE: Other protocol defined Inclusion/Exclusion criteria apply.
