Inclusion Criteria:

          -  Disease indication

               -  Participants must have histologically or cytologically confirmed metastatic or
                  unresectable solid malignancy within one of the tumor types listed below
                  (dependent on study part). Participants must have disease that is relapsed or
                  refractory or be intolerant to standard-of-care therapies and should have no
                  appropriate standard-of-care therapeutic option.

          -  Non-small cell lung cancer (NSCLC)

          -  Head and neck squamous cell cancer (HNSCC)

          -  Advanced HER2-negative breast cancer

          -  Esophageal squamous cell carcinoma (ESCC)

          -  Cutaneous squamous cell cancer (cSCC)

          -  Exocrine pancreatic adenocarcinoma

          -  Bladder cancer

          -  Cervical cancer

          -  Gastric cancer

          -  High grade serous ovarian cancer (HGSOC)

          -  Participants enrolled in the following study parts should have a tumor site accessible
             for biopsy and agree to biopsy as follows:

               -  Disease-specific expansion cohorts, participant 13 onwards: pre-treatment biopsy

               -  Biology expansion cohort: pre-treatment biopsy and additional on-treatment biopsy
                  during Cycle 1

          -  An Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1

          -  Measurable disease per the RECIST v1.1 at baseline

        Exclusion Criteria

          -  History of another malignancy within 3 years before first dose of study drug, or any
             evidence of residual disease from a previously diagnosed malignancy. Exceptions are
             malignancies with a negligible risk of metastasis or death.

          -  Known active central nervous system metastases. Participants with previously treated
             brain metastases may participate provided they:

               -  are clinically stable for at least 4 weeks prior to study entry after brain
                  metastasis treatment,

               -  have no new or enlarging brain metastases, and

               -  are off of corticosteroids prescribed for symptoms associated with brain
                  metastases for at least 7 days prior to first dose of study drug.

          -  Carcinomatous meningitis

          -  Previous receipt of an MMAE-containing agent or an agent targeting integrin beta-6

          -  Pre-existing neuropathy Grade 2 or greater per the National Cancer Institute's Common
             Terminology Criteria for Adverse Events, version 5.0 (NCI CTCAE v5.0)

          -  Any uncontrolled Grade 3 or higher (per NCI CTCAE v5.0) viral, bacterial, or fungal
             infection within 2 weeks prior to the first dose of SGN-B6A.

               -  Routine antimicrobial prophylaxis is permitted