Key Inclusion Criteria:

        Dose Escalation Part:

        • Subject with locally advanced or metastatic solid tumor(s) (excluding subjects with
        primary central nervous system [CNS] tumors), who has experienced disease progression while
        on standard therapy or is intolerant of, or not eligible for, standard therapy.

        Expansion Part:

        • Must have an advanced or metastatic, pathologically confirmed diagnosis of one of the
        following tumors: Uterine Cancer, Prostate Cancer, Esophageal Cancer, Triple Negative
        Breast Cancer (TNBC), Squamous Cell Carcinoma of the Head and Neck (SCCHN), Non-small Cell
        Lung Cancer (both adenocarcinoma (ACC) and squamous cell carcinoma (SCC) (NSCLC/ACC and
        NSCLC/SCC), Bladder Cancer.

        Both Parts:

          -  Must sign an informed consent form (ICF) indicating that he or she understands the
             purpose of, and procedures required for the trial, and is willing to participate in
             the trial prior to any trial related assessments or procedures.

          -  Must have measurable disease according to response assessment criteria relevant to the
             tumor type.

          -  Must have an Eastern Cooperative Oncology Group Performance Status (ECOG-PS) score of
             0-1 at Screening and on C1D1.

          -  A woman of reproductive potential must agree to use adequate contraception during the
             trial and for 4 months after the last GEN1044 administration. Adequate contraception
             is defined as highly effective methods of contraception.

        Key Exclusion Criteria (both parts):

          1. Has an uncontrolled intercurrent illness, including but not limited to:

               1. Ongoing or active infection requiring intravenous treatment with anti-infective
                  therapy

               2. Symptomatic congestive heart failure (grade III or IV as classified by the New
                  York Heart Association), unstable angina pectoris or cardiac arrhythmia.

               3. Uncontrolled hypertension defined as systolic blood pressure ≥160 mmHg and/or
                  diastolic blood pressure ≥100 mmHg, despite optimal medical management.

               4. Ongoing or recent evidence of significant autoimmune disease Subjects with a
                  history of grade 3 or higher irAEs that led to treatment discontinuation.

               5. Subjects with a prior history of myositis, Guillain-Barré syndrome, or myasthenia
                  gravis of any grade.

               6. History of chronic liver disease or evidence of hepatic cirrhosis.

               7. History of non-infectious pneumonitis that has required steroids, or currently
                  has pneumonitis.

               8. History of organ allograft (except for corneal transplant) or autologous or
                  allogeneic bone marrow transplant, or stem cell rescue within 3 months prior to
                  the first dose of GEN1044.

               9. Serious, non-healing wound, skin ulcer (of any grade), or bone fracture.

          2. Any history of intracerebral arteriovenous malformation, cerebral aneurysm, new or
             symptomatic brain metastases or stroke.

          3. Prior therapy:

             Radiotherapy: Radiotherapy within 14 days prior to first GEN1044 administration.
             Palliative radiotherapy will be allowed.

          4. Treatment with an anti-cancer agent (within 28 days or after at least 5 half-lives of
             the drug, whichever is shorter), prior to GEN1044 administration. Toxicities from
             previous anti-cancer therapies that have not resolved.

          5. Has a history of ≥ grade 2 cytokine release syndrome (CRS) with other CD3-based
             bispecifics, or a history of ≥ grade 3 allergic reactions to monoclonal antibody
             therapy as well as known or has known allergies, hypersensitivity, or intolerance to
             GEN1044 or its excipients.