New combo therapy hopes to tackle rare skin cancer

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guideline * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: \>= 18 years * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Histologically confirmed mycosis fungoides (MF) or Sezary syndrome (SS). Safety lead-in: \>= stage IIB OR \>= stage IB-IIA folliculotropic/transformed MF. Phase 2: \>= stage IB * Stage of disease according to Tumor-Node-Metastasis-Blood (TNMB) classification * Pathology report must be diagnostic or be consistent with MF/SS criteria * SS is defined as meeting T4 plus B2 criteria; where the biopsy of erythrodermic skin may only reveal suggestive but not diagnostic histopathologic features, the diagnosis may be based on either node biopsy or fulfillment of B2 criteria * For MF where the histological diagnosis by light microscopic examination is not confirmed, diagnostic criteria that been recommended by the International Society of Cutaneous Lymphomas (ISCL) should be used. * Measurable disease per Modified Severity Weighted Assessment Tool (mSWAT) and/or Sezary count * Baseline skin biopsy taken within 6 months available for central review submission * Without bone marrow involvement: Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: ANC \>= 1,000/mm\^3 (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets \>= 100,000/mm\^3 (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * With bone marrow involvement: Platelets \>= 75,000/mm3 (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease)(performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * Aspartate aminotransferase (AST) =\< 2.5 x ULN (unless has Gilbert's disease)(performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * Alanine aminotransferase (ALT) =\< 2.5 x ULN (unless has Gilbert's disease)(performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (unless has Gilbert's disease) (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (performed within 7 days prior to day 1 of protocol therapy unless otherwise stated) * Hepatitis C virus (HCV)\*, active hepatitis B virus (HBV) (surface antigen negative), and syphilis (rapid plasma reagin \[RPR\]) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed * Meets other institutional and federal requirements for infectious disease titer requirements * Note Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy * Subjects with MF and a history of staphylococcus colonization are eligible provided they continue to receive stable doses of prophylactic antibiotics * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 3 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Prior mogamulizumab * Any systemic therapy, including monoclonal antibody within 28 days or 5 half-lives (whichever is shorter) of initiating protocol therapy * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy * Any skin-directed therapy within 14 days prior to initiating protocol therapy * Any radiation therapy within 21 days prior to initiating protocol therapy * Immunosuppressive medication within 14 days prior to the first dose of study treatment. The following are exceptions to this criterion: * Intranasal, inhaled, topical or local steroid injections (e.g., intra-articular injection) and are on stable dose for at least 28 days * Systemic corticosteroids at physiologic doses of \< 10 mg/day of prednisone or equivalent * Live, attenuated vaccine within 30 days prior to the first dose protocol therapy * Disease free of prior malignancies for \>= 5 years with the exception of: * Currently treated squamous cell and basal cell carcinoma of the skin, or * Carcinoma in situ of the cervix, or * Surgically removed melanoma in situ of the skin (stage 0) with histological confirmed free margins of excision, or * Prostate cancer (T1a or T1b using the TNM \[tumor, nodes, metastasis\] clinical staging system) that has/have been surgically cured, or * Any other malignancy that has/have been curatively treated with surgery and/or localized radiation * Active infection requiring antibiotics * Known hepatitis B or hepatitis C infection * Other active malignancy * Females only: Pregnant or breastfeeding * Prior stem cell transplantation * Acute infection requiring systemic treatment * Conditions requiring chronic steroid or immunosuppressive treatment that likely need additional steroid or immunosuppressive treatments in addition to the protocol therapy * Renal failure requiring hemodialysis or peritoneal dialysis * Unstable cardiac disease as defined by one of the following: * Cardiac events such as myocardial infarction (MI) within the past 6 months * NYHA (New York Heart Association) heart failure class III-IV * Uncontrolled atrial fibrillation or hypertension * Major surgery (as defined by the investigator) within the 28 days prior to the first dose of study treatment * Active or prior documented autoimmune or inflammatory disorders requiring therapy within the past 3 years prior to the start of treatment. The following are exceptions to this criterion: * Vitiligo or alopecia * Hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement; or * Psoriasis not requiring systemic treatment * History of primary immunodeficiency * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures. * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)