Inclusion Criteria:

   - Patients must have histological or cytological confirmed malignancy in the following
   disease groups: melanoma, non-small cell lung carcinoma, renal cell carcinoma or
   squamous cell head and neck carcinoma, for which no standard effective or curative
   options are available

   - Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1

   - Documented evidence of disease progression during 6 month period prior to the time of
   enrollment

   - Prior therapy requirements:

      - At least >= 1 prior completed chemotherapy regimen including chemotherapy,
      biologic, immunologic or targeted therapy

      - At least 4 weeks from last dose of prior chemotherapy with resolution of the
      acute toxic effects of the therapy

      - At least 2 weeks from completion of prior radiation therapy

      - At least 4 weeks from last dose of prior investigational therapy

      - Not receiving any current anti-cancer therapy

      - At least 4 weeks from last dose of interferon or IL-2 therapy

      - At least 8 weeks from completion of antibody therapy with anti-checkpoint
      antibodies, such as anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA4) and
      anti-programmed cell death 1 (PD1)

      - At least 4 weeks from last dose of prior other biologic agents

   - Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (Karnofsky > 70%)

   - Absolute lymphocytes > 500/mcL

   - Absolute neutrophil count > 1,000/mcL

   - Platelets > 100,000/mcL

   - Total bilirubin within normal institutional limits

   - Prothrombin time (PT)/partial thromboplastin time (PTT) < 1.5 x upper limit of normal
   (ULN)

   - Hemoglobin (Hgb) > 9 g/dL

   - Alkaline phosphatase =< 2.5 x ULN

   - Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
   [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
   < 2 x institutional upper limit of normal

   - Serum creatinine < 1.5 x ULN or creatinine clearance > 60 mL/min/1.73 m^2 for patients
   with creatinine levels above institutional normal

   - No known central nervous system (CNS) metastases or neurological symptoms possibly
   related to active CNS metastasis

   - Females of childbearing potential must have a negative pregnancy test within 48 hours
   prior to initiation of protocol therapy; NOTE: subjects are considered not of child
   bearing potential if they are surgically sterile, they have undergone a hysterectomy,
   bilateral tubal ligation, or bilateral oophorectomy or they are postmenopausal;
   menopause is the age associated with complete cessation of menstrual cycles, menses,
   and implies the loss of reproductive potential; by a practical definition, it assumes
   menopause after 1 year without menses with an appropriate clinical profile at the
   appropriate age; women of child-bearing potential and men must agree to use adequate
   contraception (hormonal or barrier method of birth control; abstinence) from the time
   the consent is signed and for the duration of study participation; 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; women of
   child-bearing potential and men treated or enrolled on this protocol must also agree
   to use adequate contraception (hormonal or barrier method of birth control;
   abstinence) 4 months after completion of rhIL15

   - Ability to understand and the willingness to sign a written informed consent document

   - No history of any hematopoietic malignancy

   - No active (as defined by requiring immunosuppressive therapy) or history of clinically
   significant autoimmune disease (as defined by previously requiring immunosuppressive
   therapy)

   - No evidence of a clinically significant active infection

   - No systemic or inhaled corticosteroids within 7 days prior to initiation of protocol
   therapy; NOTE: use of topical corticosteroids and/or eye drops containing
   glucocorticosteroids is acceptable

   - No immunosuppressive therapy within 30 days prior to initiation of protocol therapy

   - No history of severe asthma, as defined by prior or current use of systemic
   corticosteroids for disease control, with the exception of physiological replacement
   doses of cortisone acetate or equivalent, as defined by a dose of 10 mg or less; NOTE:
   history of mild asthma not requiring daily therapy is eligible

   - No history of pulmonary disease such as emphysema or chronic obstructive pulmonary
   disease (COPD), (forced expiratory volume in one second [FEV1] > 2L or >= 50% of
   predicted for height and age); pulmonary function tests (PFTs) are required in
   patients with significant pulmonary or smoking history

   - No history of human immunodeficiency virus (HIV), active or chronic hepatitis B,
   hepatitis C or human T-cell lymphotropic virus (HTLV-I) infection; NOTE: a positive
   hepatitis B serology indicative of previous immunization (i.e., hepatitis B surface
   antibody [HBsAb] positive and hepatitis B core antibody [HBcAb] negative), or a fully
   resolved acute hepatitis B virus (HBV) infection is not an exclusion criterion

   - Females of childbearing potential and males must be willing to use an effective method
   of contraception (hormonal, barrier method of birth control or abstinence) from the
   time the consent is signed, during the duration of study participation and 4 months
   after discontinuation of protocol therapy

   - Females must not be breastfeeding

   - No evidence of clinically significant congestive heart failure, (ejection fraction of
   45% or greater)

   - No platelet or blood transfusions within two weeks of obtaining baseline laboratory
   values

   - No blood modifiers while enrolled in the study (i.e., growth factors such as
   erythropoiesis-stimulating agent [ESA] or filgrastim [G-CSF]); NOTE: blood
   transfusions are allowed per institutional guidelines

Exclusion Criteria:

   - Patients who have had chemotherapy within 4 weeks (6 weeks for nitrosoureas or
   mitomycin C), or radiotherapy within 2 weeks prior to entering the study or those who
   have not recovered from adverse events due to agents administered more than 4 weeks
   earlier

   - Class II or greater congestive heart failure as described in the New York Heart
   Association Functional Classification criteria

   - Patients with thyroid disease should be excluded unless their T4 is normal or they are
   on replacement therapy

   - Patients with primary brain cancer or known brain metastases should be excluded from
   this clinical trial

   - Patients who have received prior anti-CTLA4 or anti-PD1 therapy less than 8 weeks
   prior to enrollment

   - Patients who have received prior biologic agents less than 4 weeks prior to enrollment

   - Patients who have received prior interferon or IL-2 therapy less than 4 weeks prior to
   enrollment

   - ECOG score greater than 1 (Karnofsky < 70%)

   - HIV-positive patients

   - Positive hepatitis C serology

   - Patients who are receiving any other investigational agents

   - Inability to home monitor blood pressure

   - Uncontrolled intercurrent illness including, but not limited to, ongoing or active
   infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
   arrhythmia, or psychiatric illness/social situations that would limit compliance with
   study requirements