Inclusion Criteria:

          1. Has a histologically or cytologically documented, advanced (metastatic and/or
             unresectable) cancer as listed below that is incurable: Note: Prior neoadjuvant or
             adjuvant therapy included in initial treatment may not be considered first- or
             later-line standard of care treatment unless such treatments were completed less than
             12 months prior to the current tumor recurrence.

             A. Non-squamous NSCLC for which prior standard first-line treatment containing an
             anti-programmed cell death protein 1/programmed cell death protein 1 ligand
             (PD-1/PD-L1) checkpoint inhibitor (CPI) alone or in combination has failed and that
             has progressed to no more than 1 prior systemic therapy. In Phase 2, participants with
             non-squamous NSCLC must have not received more than 1 prior systemic therapy and must
             not have presented with disease progression during the first 5 months of treatment
             with first-line CPI/anti-PD-(1/L1)-containing therapy.

             Note: In Phase 1, participants with non-squamous NSCLC and known driver
             mutations/genomic aberrations (eg, EGFR, B-Raf proto-oncogene mutation V600E [BRAF
             V600E], and ROS proto-oncogene 1 [ROS1] sensitizing mutations, neurotrophic receptor
             tyrosine kinase [NRTK] gene fusions, and anaplastic lymphoma kinase [ALK]
             rearrangements) must have also shown progressive disease after treatment with a
             commercially available targeted therapy. In Phase 2, participants with driver
             mutations are not eligible.

             B. CPI-naive cervical cancer (squamous cell carcinoma, adenosquamous carcinoma or
             adenocarcinoma of the cervix) participants for whom prior standard first-line
             treatment has failed and who have received no more than 1 prior systemic line of
             therapy for recurrent or Stage IVB cervical cancer. Note: The following cervical
             tumors are not eligible: minimal deviation/adenoma malignum, gastric-type
             adenocarcinoma, clear-cell carcinoma, and mesonephric carcinoma. Histologic
             confirmation of the original primary tumor is required via pathology report. Note:
             First-line treatment must have consisted of platinum-containing doublet. Chemotherapy
             administered concurrently with primary radiation (e.g., weekly cisplatin) is not
             counted as a systemic chemotherapy regimen.

             C. CPI-naïve microsatellite stable-colorectal cancer (MSS-CRC) participants for whom
             prior standard first-line treatment has failed and who have progressed on no more than
             3 chemotherapy regimens.

             Note: Participants must have received prior treatment with fluoropyrimidine-,
             oxaliplatin-, and irinotecan-containing regimens if indicated.

             D. Unresectable Stage III or Stage IV cutaneous melanoma that has not received prior
             therapy with a CPI in the metastatic setting.

             E. Squamous NSCLC for which prior standard first-line treatment containing an
             anti-PD-(1/L1) checkpoint inhibitor alone or in combination has failed. Participant
             must have not received more than 1 prior systemic therapy and must not have presented
             with disease progression during the first 5 months of treatment with first-line
             CPI/anti-PD-(1/L1)-containing therapy.

             F. SCLC that has progressed during or after first-line platinum-based chemotherapy
             regimen or equivalent if platinum-based therapy is contraindicated.

             G. HNSCC (oral cavity, pharynx, larynx) not amenable to local therapy with curative
             intent that has progressed:

               -  Within 6 months of the last dose of platinum therapy in the adjuvant (ie, with
                  radiation after surgery) or primary (ie, with radiation) settings, or

               -  On or after 1 prior systemic immune CPI/anti-PD-(1/L1)-containing therapy in the
                  metastatic setting. HNSCC participant must have not received more than 1 prior
                  systemic therapy and must not have presented with disease progression during the
                  first 5 months of treatment with first-line CPI/anti-PD-(1/L1)-containing
                  therapy. H. Treatment-naïve MSI-H/dMMR CRC.

          2. Has at least 1 radiologically measurable lesion based on RECIST, Version 1.1. Tumor
             lesions situated in a previously irradiated area are considered measurable if
             progression has been demonstrated in such lesions.

          3. Has a performance status of 0 or 1 on the Eastern Cooperative Group Oncolgy (ECOG)
             Performance Scale.

          4. Has left ventricular ejection fraction (LVEF) ≥40%; as measured by echocardiogram
             (ECHO) or multiple-gated acquisition (MUGA) scan.

          5. Has recovered to Grade 1 or baseline from all toxicity associated with previous
             therapy or have the toxicity established as sequela. Note: Has a neuropathy ≤Grade 2,
             any grade alopecia, or autoimmune endocrinopathies with stable replacement therapy are
             permitted.

          6. Demonstrate adequate organ function as described below:

        A. Platelet count ≥75.0 × 10^9/L. B. Absolute neutrophil count (ANC) ≥1.0 × 10^9/L. C.
        Hemoglobin ≥85 g/L (red blood cell [RBC] transfusion allowed ≥14 days before assessment).

        D. Estimated creatinine clearance using the Cockcroft-Gault formula ≥45 mL/minute for
        participants with serum creatinine concentrations above the upper limit of normal (ULN).

        E. Aspartate aminotransferase (AST, GOT) and alanine aminotransferase (ALT, GPT) ≤3.0 ×
        ULN; bilirubin ≤1.5 × ULN. Participants with Gilbert's syndrome may have a bilirubin level
        >1.5 × ULN, per discussion between the investigator and the medical monitor.

        Exclusion Criteria:

          1. Received extended field radiotherapy ≤4 weeks before the start of treatment (≤7 days
             for limited field radiation for palliation outside the chest or brain).

          2. History of uncontrolled brain metastasis (evidence of progression by imaging over a
             period of 4 weeks and/or neurologic symptoms that have not returned to baseline).
             Participant with treated brain metastases are allowed provided they are radiologically
             stable, without evidence of progression for at least 4 weeks by repeat imaging,
             clinically stable, and without requirement of steroid treatment for at least 14 days
             prior to first dose of study treatment. Note: For asymptomatic participants, screening
             brain imaging is not required.

          3. Second malignancy within the previous 3 years, except treated basal cell or localized
             squamous skin carcinomas, localized prostate cancer, cervical carcinoma in situ,
             resected colorectal adenomatous polyps, breast cancer in situ, or other malignancy for
             which the participant is not on active anticancer therapy.

          4. Major surgery ≤14 days from the first dose of study drug and not recovered fully from
             any complications from surgery.

          5. History of immune-related adverse events (AEs) related to treatment with immune CPIs
             that required treatment discontinuation.

          6. Receiving or requires the continued use of medications that are known to be strong or
             moderate inhibitors and inducers of cytochrome P-450 (CYP) 3A4/5. To participate in
             this study, such participant should discontinue use of such agents for at least 2
             weeks (1 week for CYP3A4/5 and Pgp inhibitors) before receiving a dose of TAK-981.

          7. Had received any live vaccine (e.g., varicella, pneumococcus) within 4 weeks of
             initiation of study treatment.

          8. Baseline prolongation of the QT interval corrected using Fridericia's formula (QTcF)
             (eg, repeated demonstration of QTcF interval >480 ms, history of congenital long QT
             syndrome, or torsades de pointes).

          9. Has a history of autoimmune disease requiring systemic immunosuppressive therapy with
             daily doses of prednisone >10 mg/day or equivalent doses, or any other form of
             immunosuppressive therapy. Hormone therapy (e.g., thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not
             considered an excluded form of systemic treatment of an autoimmune disease.

         10. Has a history of noninfectious pneumonitis that required steroids or a history of
             interstitial lung disease.

         11. Has an evidence of active, non-infectious pneumonitis.

         12. Has a history of allogeneic tissue or solid organ transplant.

         13. Has an active infection requiring systemic therapy.

         14. Has a known history of HIV infection or any other relevant congenital or acquired
             immunodeficiency.

         15. Has a known hepatitis B virus surface antigen seropositive or detectable hepatitis C
             infection viral load. Note: Participants who have positive hepatitis B core antibody
             or hepatitis B surface antigen antibody can be enrolled but must have an undetectable
             hepatitis B viral load.

        16. History of any of the following ≤6 months before first dose: congestive heart failure
        New York Heart Association Grade III or IV, unstable angina, myocardial infarction,
        unstable symptomatic ischemic heart disease, uncontrolled hypertension despite appropriate
        medical therapy, ongoing symptomatic cardiac arrhythmias >Grade 2, pulmonary embolism or
        symptomatic cerebrovascular events, or any other serious cardiac condition (eg, pericardial
        effusion or restrictive cardiomyopathy). Chronic atrial fibrillation on stable
        anticoagulant therapy is allowed.

        17. Psychiatric illness/social circumstances that would limit compliance with study
        requirements and substantially increase the risk of AEs or has compromised ability to
        provide written informed consent.