The following criteria is provided for health care professionals.

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