Inclusion criteria

* Parts A, B, and C * Relapsed, locally-advanced or metastatic colorectal or pancreatic cancer, sqNSCLC, or HNSCC participants who are not candidates for standard therapy. * All participants must have experienced disease progression on or after their most recent systemic therapy. * Colorectal cancer (closed to enrollment): participants must have received prior therapy with each of following agents, if eligible: a fluoropyrimidine, oxaliplatin, irinotecan, and/or bevacizumab. Participants should have received no more than 3 systemic regimens in the metastatic setting. * sqNSCLC (closed to enrollment): Participants with NSCLC must have predominant squamous histology. Participants must have received prior therapy with a platinum-based treatment and a checkpoint inhibitor (CPI), if eligible. Participants should have received no more than 3 lines of systemic therapy in the metastatic setting. * Participants eligible for a tyrosine kinase inhibitor should have received such therapy. These participants should have received no more than 4 lines of systemic therapy in the metastatic setting. * Exocrine pancreatic adenocarcinoma (closed to enrollment): Participants with exocrine pancreatic adenocarcinoma must have predominant adenocarcinoma histology. Participants must have received prior therapy with a gemcitabine-based or 5FU-based regimen, if eligible, and should have received no more than 1 systemic regimen in the unresectable or metastatic setting. * HNSCC (closed to enrollment): Participants with HNSCC in Part C must have received prior therapy with a platinum-based regimen and/or a checkpoint inhibitor (CPI), if eligible, and must have experienced disease progression following such therapy. Participants should have received no more than 3 systemic lines of therapy in the recurrent or metastatic setting. * Part E * Participants with HNSCC must have experienced disease progression on or after their most recent systemic therapy. Participants should have received no more than 1 or 2 systemic lines of therapy in the recurrent/metastatic setting as specified below. Participants must have received a platinum-based regimen and a PD-(L)1 inhibitor. * Parts D, F, and G * Part D is closed to enrollment. Part F and Part G will enroll only participants with HNSCC. * Participants with HNSCC must have received no previous systemic therapy in the recurrent or metastatic disease setting. * Part D only * Participants with NSCLC must have histologically or cytologically documented squamous cell NSCLC and must have received no previous systemic therapy for metastatic disease or radiation therapy to the lung that is \> 30 Gy within 6 months of the first dose of study treatment. * PD-L1 biomarker expression as determined by a PD-L1 IHC assay should be available * Part F only * Participants must have CPS ≥1 by local PD-L1 IHC assay to be eligible for enrollment. Participants must be able to submit a tissue sample for retrospective PD-L1 testing. Tissue may be fresh biopsy or archival, collected within 2 years of Cycle 1 Day 1. * Part G only * Non-EU eligibility criteria: No CPS requirement for the cohort evaluating tisotumab vedotin in combination with pembrolizumab and carboplatin. * EU-specific eligibility criteria: Participants must have a CPS ≥1 by local PD-L1 IHC assay. * Participants must be able to submit a tissue sample for retrospective PD-L1 testing. Tissue may be fresh biopsy or archival, collected within 2 years of Cycle 1 Day 1. * Baseline measurable disease as measured by RECIST v1. 1. * Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0 or 1.