Mogamulizumab and Brentuximab Vedotin in CTCL and Mycosis Fungoides

Inclusion Criteria: 1. Able to understand and comply with study procedure, understand the risks involved in the study and provide written informed consent before the first study-specific procedure 2. Men or women \>18 years with pathologically confirmed diagnosis of Sezary Syndrome or Mycosis fungoides 3. Must have CD30 positivity on recent biopsy of \>1% 4. Stage II-IV, for skin only disease \>20% BSA should be involved, large cell transformation is allowed. 5. Must have received at least one prior systemic therapy like bexarotene, interferons, ECP, methotrexate, Gemcitabine, Vorinostat etc. (patients who have received only skin directed therapy are not allowed) 6. ECOG performance status of 0,1 or 2 7. Adequate organ function at screening defined as follows * Hepatic: T bili \<2 X ULN, isolated bilirubin of \>2 is accepted if there is suspected diagnosis of Gilbert's syndrome, AST and ALT \<3X ULN * Renal: estimated GFR \>40 mL/Min/1.73 m2 * Cardiac: LVEF \>40% 8. Patients must have completed any chemotherapy, radiation therapy, or biologic therapy specific to their neoplasm ≥ 1 weeks or 5 half-lives (whichever is longer). Radiation for palliation on symptomatic lesions has no wash out period. 9. Expected life ≥ 4 months 10. Participants with a prior history of stem cell transplant (autologous and/or allogeneic) are allowed if all of the following are met: * 180 days or more have elapsed from the time of transplant * subject has been off systemic immunosuppressive medications (including but not limited to: cyclosporine, tacrolimus, mycophenolate mofetil, or corticosteroids) for at least 30 days prior to C1D1. Topical steroids are permitted. * no signs or symptoms of acute graft versus host disease, other than Grade 1 skin involvement. * there are no signs or symptoms of chronic graft versus host disease * requiring systemic therapy 11. Women of child-bearing potential (according to recommendations of the Clinical Trial Facilitation Group \[CTFG\], CTFG 2014) must not be pregnant or breastfeeding and must have a negative pregnancy test at screening. A woman is considered of childbearing potential (ie, fertile) following menarche and until becoming postmenopausal, unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. A man is considered fertile after puberty unless permanently sterile by bilateral orchidectomy. 12. Subjects and their partners with reproductive potential must agree to use 2 highly effective contraceptive measures during the study and must agree not to become pregnant or father a child for 3 months after the last dose of study treatment. Contraceptive measures that may be considered highly effective comprise combined hormonal contraception (oral, vaginal, or transdermal) or progestogen-only hormonal contraception (oral, injectable, implantable) associated with inhibition of ovulation, intrauterine device, intrauterine hormone-releasing system, bilateral tubal occlusion, sexual abstinence, and surgically successful vasectomy. Abstinence is acceptable only if it is consistent with the preferred and usual lifestyle of the subject. Periodic abstinence (eg, calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not acceptable methods of birth control. Exclusion Criteria: 1. Prior exposure of BV \< 6 months ago, or Moga. Prior exposure of BV is allowed if it is \>6 months ago and CD30+ in \>1% of in biopsy after last BV 2. Active CNS involvement by MF/Sezary Syndrome 3. Should not be receiving any other investigational agents. Prior use of investigational agents or other systemic therapy is allowed if it is \>1 week ago or 5x half-life of the investigational agent whichever is shorter. 4. Pregnant and lactating women 5. Patients with clinically significant illness which would compromise participation in the study. 6. Severe or uncontrolled systemic infection. (active skin infections in CTCL/MF patients are allowed once course of antibiotics is completed and infection is under control) 7. Known HIV infection 8. Active Hepatitis B or C infection with active virus detected in blood. Hepatitis B core positive and HBsAg positivity are allowed if HBV DNA in blood is negative. Patient should be on antiviral prophylaxis. Hepatitis C positivity is allowed but HCV DNA by PCR must be negative in peripheral blood. 9. Uncontrolled DM, HTN, NYHA Grade III-IV CHF, unstable angina, Myocardial infarction within past 3 months, uncontrolled cardiac arrhythmia, uncontrolled psychiatric illness/social situation that would limit compliance with study requirements in the opinion of the investigator. 10. Grade 2 or more peripheral sensory or motor neuropathy 11. Prior severe allergic or anaphylactic reaction to monoclonal antibody or BV. 12. History of solid organ transplant 13. History of a second malignancy, excluding non-melanoma skin cell cancer within past 2 years.