Study of Mogamulizumab + Docetaxel in Subjects With Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed Stage IIIB or IV advanced or metastatic NSCLC with measurable neoplastic disease. Sputum cytology alone is not considered an acceptable method of diagnosis; * Prior therapy must meet all of the following criteria: 1. Subject has experienced disease progression or unacceptable toxicity/intolerance after receiving at least 1 systemic platinum-containing regimen; 2. Subject with a tumor of non-squamous histology must be tested for epidermal growth factor receptor (EGFR) mutations and anaplastic lymphoma kinase (ALK) rearrangement. Subject with EGFR activating mutation or ALK rearrangement must have experienced disease progression or unacceptable toxicity/intolerance after receiving at least one EGFR tyrosine kinase inhibitor or ALK inhibitor; 3. Subject has received PD-1/PD-L1 blockade or has been informed of the results of relevant positive Phase 3 trials with these agents. * Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1 at baseline; * Minimum life expectancy of 3 months; * Agrees to use a medically effective method of contraception. Male subjects and women of child-bearing potential (WOCBP) must agree to use effective contraception, e.g., oral contraceptives, double barrier method (condom plus spermicide or diaphragm plus spermicide), or practice true abstinence from sexual intercourse during the study and for 3 months after the last dose. Women of child-bearing potential include female subjects who have experienced menarche and have not undergone surgical sterilization or are not postmenopausal (defined as amenorrhea ≥ 12 consecutive months without an alternative medical cause); * WOCBP must have a negative serum pregnancy test within 7 days prior to receiving investigational product and a negative urine pregnancy test on Day 1 of each Cycle; * Recovered (i.e., Grade ≤ 1 or to a baseline level) from the effects of recent surgery, radiotherapy, chemotherapy, hormonal therapy, or other therapies for cancer (with the exception of alopecia for which no resolution is required and peripheral neuropathy which must have resolved to Grade ≤ 1 for subjects receiving prior taxane-based chemotherapy); * Adequate organ function defined as below: 1. Total bilirubin ≤ upper limit of normal (ULN); 2. Hemoglobin (Hgb) ≥ 9.0 g/dL; 3. Serum creatinine (sCr) ≤ 1.5 x ULN; 4. Absolute neutrophil count (ANC) ≥ 1500 cells/mm3; 5. Platelets ≥ 100 × 109/L; * Sufficient archived tumor samples (if taken within 6 months prior to treatment may be submitted) available for PD assessments, or willingness to undergo a pre-treatment core needle biopsy, preferably of the primary tumor, in order to obtain such tissue; * Willing and able to undergo a post-dose core needle biopsy. Exclusion Criteria: * Prior treatment with docetaxel or mogamulizumab; * Requires administration of a prohibited medication or treatment; * Has a significant uncontrolled intercurrent illness including, but not limited to: 1. Ongoing or active infection requiring antibiotics; 2. Clinically significant cardiac disease (class III, or IV of the New York Heart Association classification; unstable angina pectoris, myocardial infarction within 6 months or is post angioplasty or stenting within 6 months; clinically significant cardiac arrhythmia, or uncontrolled hypertension (i.e., systolic blood pressure \> 150 mm Hg, diastolic blood pressure \> 90 mmHg) despite anti-hypertensive medication; 3. Uncontrolled diabetes, active liver disease, poorly controlled chronic obstructive pulmonary disease, serious or non-healing wound, ulcer, or fracture; 4. Known or tests positive for human immunodeficiency virus, hepatitis B, or hepatitis C 5. Active known auto-immune disease with the exception of autoimmune thyroiditis, vitiligo, and alopecia; 6. Pleural effusion requiring repetitive drainage, i.e., an indwelling catheter or 2 thoracenteses with 6 weeks of the first dose of mogamulizumab; * Received monoclonal antibodies (for any reason), chemotherapy, surgery, investigational therapy, or radiotherapy within 14 days of the first dose of mogamulizumab; * Received live, attenuated vaccine within 28 days prior to the first dose of mogamulizumab; * Use of immunosuppressive medication within 14 days before the first dose of mogamulizumab. Note: Inhaled, intranasal, intra-articular, or topical corticosteroids are allowed. Non-immunosuppresive doses of systemic steroids for adrenal replacement or for contrast allergy are allowed;; * Any history or signs of central nervous system metastases; * Any history or signs of pulmonary lymphangitic spread; * Experienced a Grade 3 or higher hypersensitivity reaction to monoclonal antibodies or other therapeutic proteins, and the reaction could not be controlled or prevented on subsequent infusion with standard therapies such as antihistamines, 5-hydroxytryptamine (5-HT3) receptor antagonists, or corticosteroids; * The subject has a history of severe hypersensitivity reactions to drugs formulated with polysorbate 80; * History of second primary cancer within the past 5 years, with the exception of: 1. Curatively resected non-melanomatous skin cancer; 2. Curatively treated cervical intraepithelial neoplasia or prostate carcinoma with current prostate specific antigen (PSA) \< 0.01 ng/mL; or 3. Curatively treated ductal carcinoma in situ of the breast; * The subject is pregnant or breastfeeding. * The subject has aspartate aminotransferase and/or alanine aminotransferase \> 1.5 × ULN, with concomitant alkaline phosphatase \> 2.5 × ULN.