-INCLUSION CRITERIA:

          1. Patients must have one of the following histologically or cytologically proven
             relapsed and/or refractory to at least one line of systemic treatment, T-cell
             malignancies confirmed by the Laboratory of Pathology, NCI: mycosis fungoides/Sezary
             syndrome, or adult T-cell leukemia (chronic, acute, or lymphoma subtype by Shimoyama
             criteria)

          2. Patients with CD30+ MF/SS must have relapsed after or become intolerant to treatment
             with brentuximab vedotin

          3. A formalin fixed tissue block or 15 slides of tumor sample (archival or fresh) must be
             available for performance of correlative studies. NOTE: Patients must be willing to
             have a tumor biopsy if prior tissue or adequate archival tissue is not available
             (i.e., post- enrollment and prior to treatment).

          4. Disease must be measurable with at least one measurable lesion by RECIL 2017 or mSWAT
             criteria, or have an abnormal clonal T-cell population detectable by peripheral blood
             flow cytometry

          5. Age >18 years

             NOTE: Because no dosing or adverse event data are currently available on the use of
             rhIL-15 in combination with mogamulizumab in patients <18 years of age, children are
             excluded from this study, but will be eligible for future pediatric trials

          6. ECOG performance status less than or equal to 1 (Karnofsky greater than or equal to
             80%

          7. Patients must have normal organ and marrow function as defined below:

               -  Absolute neutrophil count: greater than or equal to 1,000/mcL

               -  Platelets: > 100,000/mcL

               -  Total bilirubin: less than or equal to 1.5 X institutional upper limit of normal
                  (ULN)

               -  AST(SGOT)/ALT(SGPT): less than or equal to 2.5 X institutional ULN

               -  Serum creatinine: less than or equal to 1.5 X institutional ULN, OR Creatinine
                  clearance: greater than or equal to 50 mL/min/1.73 m2 for patients with
                  creatinine levels >1.5 institutional ULN

          8. Negative serum or urine pregnancy test at screening for women of childbearing
             potential (WOCBP)

             NOTE: WOCBP is defined as any female who has experienced menarche and who has not
             undergone successful surgical sterilization or who is not postmenopausal.

          9. Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry, for
             the duration of study participation, and 6 months after completion of rhIL-15 and
             mogamulizumab administration. Should a woman become pregnant or suspect she is
             pregnant while she or her partner is participating in this study, she should inform
             her treating physician immediately.

         10. Ability of subject to understand and the willingness to sign a written informed
             consent document

        EXCLUSION CRITERIA:

          1. Patients with other T-cell leukemias/lymphomas not specified in the inclusion criteria

          2. Anti-cancer treatment within 2 weeks of the first dose of rhIL-15 and mogamulizumab (4
             weeks for anti-cancer monoclonal antibody or investigational agents, 6 weeks for donor
             lymphocyte infusion,100 days for allogeneic stem cell transplant)

          3. Systemic treatment for acute or chronic graft versus host disease (GVHD) within 12
             weeks of the first dose of rhIL-15 and mogamulizumab

          4. Cohort 1 (Dose Escalation) only: history of grade 3/4 GVHD, or active grade 1/2 GVHD
             regardless of treatment

          5. Persisting toxicity related to prior therapy of grade > 1, with the exception of the
             following: alopecia, sensory neuropathy grade less than or equal to 2, or other grade
             less than or equal to 2 not constituting a safety risk based on investigator's
             judgment

          6. Patients who are receiving any other investigational agents

          7. Current use of immunosuppressive medication, EXCEPT for the following:

               -  Intranasal, inhaled, topical steroids, or local steroid injection (e.g.,
                  intra-articular injection)

               -  Systemic corticosteroids at physiologic doses less than or equal to 10 mg/day of
                  prednisone or equivalent; or,

               -  Steroids as premedication for hypersensitivity reactions (e.g., CT scan
                  premedication)

          8. Patients with previous malignant disease other than the target malignancy within the
             last 3 years with the exception of basal or squamous cell carcinoma of the skin or
             cervical carcinoma in situ

          9. Cohort 1 (Dose Escalation) only: Active or history of any autoimmune disease thought
             to be unrelated to their malignancy; for Cohort 2 (Dose Expansion), patients with
             history of autoimmune disease who are not on active immunosuppressive therapy

         10. Patients with asthma requiring chronic inhaled or oral corticosteroids, or history of
             asthma requiring mechanical ventilation. Patients with a history of mild asthma that
             are on or can be switched to non-corticosteroid bronchodilator regimens are eligible

         11. Patients with active bacterial infections, documented HIV infection or positive HIV
             1/2 antibodies at screening, PCR evidence for active or chronic hepatitis B or
             hepatitis C, or positive screening HBV/HCV serology without documentation of
             successful curative treatment

         12. Presence of uncontrolled intercurrent illnesses including but not limited to ongoing
             or active infection, symptomatic congestive heart failure, unstable angina pectoris,
             cardiac arrhythmia, cognitive impairment, active substance abuse, or psychiatric
             illness/social situations that in the view of the Investigator would preclude safe
             treatment and limit compliance with study requirements

         13. Inability or refusal to practice effective contraception during therapy or the
             presence of pregnancy or active breastfeeding. Because there is no significant
             preclinical information regarding the risks to a fetus or a newborn infant, all
             pregnant or breastfeeding woman will be excluded from participation in this trial

         14. History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to rhIL-15 or mogamulizumab, unless felt to be in the best interests of
             the patient in the opinion of the investigator

         15. Patients who received a live vaccine within 30 days of planned start of study therapy.
             Vaccination with a live vaccine while on trial is prohibited. NOTE: Seasonal influenza
             vaccines for injection are generally inactivated flu vaccines and are allowed; however
             intranasal influenza vaccines (e.g., Flu-Mist ) are live attenuated vaccines, and are
             not allowed