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.
• No active central nervous system (CNS) involvement with NHL.
• 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 ≥ 800/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 may have 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.
• Patients with MM may have received a B cell maturation antigen (BCMA) 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 6 months washout

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.

• 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 6 months washout
• Patients who have had < 28 days since the last anti-cancer treatment, chemotherapy, biological therapy, or < 14 days from approved tyrosine kinase inhibitor therapy (sunitinib, sorafenib, vemurafenib, dabrafenib, cobimetinib), 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)