Key Inclusion Criteria:

          -  Patients must have relapsed or refractory MM or NHL with no available therapies that
             would confer clinical benefit for their primary disease.

          -  Measurable or detectable disease according to International Myeloma Working Group
             (IMWG) and the Lugano Classification. Extranodal NHL disease that is measurable by
             fluorodeoxyglucose-positron emission tomography (FDG-PET) imaging only is allowed.

          -  Estimated glomerular filtration rate (eGFR) ≥ 40 mL/min/1.73 m2.

        Patient has the following laboratory test results during Screening:

          1. Absolute neutrophil count (ANC) or absolute granulocyte count (AGC) ≥ 1000/µL

          2. Platelets ≥ 30,000/µL

          3. Hemoglobin ≥ 8g/dL

          4. Absolute lymphocytes ≥ 500/µL

          5. Leukocytes ≥ 3000/µL

        Patients are eligible who also meet all the following criteria in these cohorts of Part 2:

        Cohort A only:

        • Patients with NHL who received a commercially approved CD19 CAR-T product and had PD. The
        first dose of NKTR-255 will be administered within 30 days of the PD.

        Cohort B only:

          -  Patients with MM must have had previous exposure to proteasome inhibitor,
             immunomodulatory agent (IMiD), and anti-CD38 therapy.

          -  Patients who previously received daratumumab or other anti-CD38 therapies must have at
             least 3 months washout.

        Cohort C only:

        • Patients with relapsed or refractory iNHL who previously progressed during or following 1
        or more prior systemic rituximab-containing (or another treatment with an anti-CD20
        antibody-containing) regimens for lymphoma.

        Key Exclusion Criteria:

          -  Patients who have an active, known, or suspected autoimmune disease.

          -  Any treatment-related neurotoxicity or cytokine release syndrome (CRS) prior to
             enrollment into the study should return to baseline before NKTR-255 treatment.

          -  Active central nervous system (CNS) involvement with NHL.

          -  Patients who have been previously treated with prior interleukin-2 or interleukin-15.

          -  Patients who received daratumumab or other anti-CD38 therapies previously must have 3
             months washout.

          -  Patients who have had < 28 days since the last anti-cancer treatment, chemotherapy,
             biological therapy, or < 14 days from approved anti-myeloma agents, or systemic or
             inhaled steroid therapy at doses greater than 10 mg of prednisone or equivalent before
             administration of the first dose of study drug(s).

          -  Prolonged Fridericia's corrected QT interval (QTcF) > 450 ms for men and > 470 ms for
             women at Screening.

          -  Contraindication to or unable to receive daratumumab (Cohort B only)

        NOTE: Other protocol defined Inclusion/Exclusion criteria may apply