Triple-Drug cocktail shows promise against CLL

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

Inclusion Criteria: * Diagnosis of CLL meeting criteria established in the World Health Organization (WHO) classification of hematologic disorders * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Relapsed or refractory CLL patients must meet the following requirements: * Received at least 1 prior therapy * Require treatment in the opinion of the investigator * Relapsed patients must have developed progressive disease following a response to a prior therapy * Refractory patients must have failed to respond or relapsed within 6 months to the last prior therapy * Treatment-naïve CLL patients must meet the following requirements (Phase II only): * Symptomatic disease as defined by International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria * Received no prior chemotherapy, immunotherapy, or targeted therapy for the treatment of CLL with the exceptions of palliative loco-regional radiotherapy and corticosteroids for symptom control * Hemoglobin \>= 8 g/dL * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 40,000/mm\^3 * Prothrombin time (PT)/partial thromboplastin time (PTT) =\< 1.5 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (excepting Gilbert's syndrome) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 × ULN * Serum creatinine \< 2.0 mg/dL or creatinine clearance (Cockcroft) \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Female patients must be surgically sterile, post-menopausal (for at least 1 year), or have negative results from a pregnancy test performed as follows: * At screening, on a serum sample obtained within 14 days prior to the first study drug administration, and * Prior to dosing, on a urine sample obtained on day 1 of treatment if it has been \> 7 days since obtaining the serum pregnancy test result * All female patients not surgically sterile or post-menopausal (for at least 1 year) and non-vasectomized male patients must practice at least one of the following methods of birth control: * Total abstinence from sexual intercourse (minimum one complete menstrual cycle) * A vasectomized partner * Hormonal contraceptives for at least 2 months prior to day 1 of treatment * Double-barrier method * Non-vasectomized male patients must practice at least one of the following methods of birth control throughout the duration of study participation and for at least 3 months after study treatment: * A partner who is surgically sterile or postmenopausal (for at least 1 year) or who is taking hormonal contraceptives (oral, parenteral, vaginal ring, or transdermal) for at least 3 months prior to study drug administration * Total abstinence from sexual intercourse * Double-barrier method (condom, diaphragm or cervical cup with spermicidal, contraceptive sponge, jellies, or cream) * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, immunotherapy, radiotherapy, or investigational therapy within 28 days prior to entering the study or those who have not recovered from adverse events due to agents administered more than 28 days earlier; steroids for control of disease related symptoms are permitted * Patients who are receiving any other investigational agents * Uncontrolled autoimmune hemolytic anemia or thrombocytopenia * Active Richter's transformation * Known active involvement of the central nervous system by lymphoma or leukemia * Patients who require warfarin anticoagulation or who have received warfarin or equivalent vitamin K antagonists =\< 7 days prior to treatment day 1; patients may be eligible if able to be taken off warfarin and started on an alternative anticoagulant * Received potent cytochrome P450 3A4 (CYP3A4) inhibitors (such as fluconazole, ketoconazole, and clarithromycin) within 7 days prior to the first dose of study treatment * Received potent CYP3A4 inducers (such as rifampin, carbamazepine, phenytoin, St. John's wort) within 7 days prior to the first dose of study treatment * Consumed grapefruit or grapefruit products, Seville oranges (including marmalade containing Seville oranges), or star fruit within 3 days prior to the first dose of study treatment * History of a prior significant toxicity, other than thrombocytopenia, from another Bcl-2 family protein inhibitor * Known cysteine-481 Bruton's tyrosine kinase (BTK) mutation or CLL refractory to or progressed during ibrutinib or other Cys-481 binding BTK inhibitor treatment * Known infection with the human immunodeficiency virus (HIV) virus * A cardiovascular disability status of New York Heart Association class \>= 2, defined as cardiac disease in which patients are comfortable at rest but ordinary physical activity results in fatigue, palpitations, dyspnea, or angina pain * Positive hepatitis serology: * Hepatitis B virus (HBV): patients with positive serology for hepatitis B defined as positivity for hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (anti-HBc); patients who are positive for anti-HBc may be considered for inclusion in the study on a case-by-case basis if they are hepatitis B viral deoxyribonucleic acid (DNA) negative and are willing to undergo ongoing HBV DNA testing by real-time polymerase chain reaction (PCR); patients with positive serology may be referred to a hepatologist or gastroenterologist for appropriate monitoring and management * Patients with positive HBSAg consistent with prior vaccination to HBV (i.e., anti-HBs+, anti-HBc-) may participate * Patients suspected to have false positive serologic studies because of IV immunoglobulin administration are potentially eligible after negative PCR studies for viral DNA/ribonucleic acid (RNA) and discussion with the principal investigator * Hepatitis C (HCV): patients with positive hepatitis C serology unless HCV RNA is confirmed negative and may be considered for inclusion in the study on a case-by-case basis (e.g., patients with negative viral load after HCV-specific treatment) * History of severe (defined as grade 4 and/or requiring permanent discontinuation of prior antibody therapy) allergic or anaphylactic reactions to human, humanized, chimeric, or murine monoclonal antibodies * Patients who received a live viral vaccination within 6 months prior to the first dose of study drug * A female patient who is pregnant or breast-feeding * 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 * History of other active malignancies other than CLL within the past 3 years prior to study entry, with the exception of: * Adequately treated in situ carcinoma or the cervix uteri or breast * Basal cell or localized squamous cell carcinoma of the skin * Previous malignancy confirmed and surgically resected (or treated with other modalities) with curative intent or without relapse for \>= 2 years * Vaccination with a live vaccine \< 28 days prior to the start of treatment * Inability to swallow capsules or tablets, or disease significantly affecting gastrointestinal function and/or inhibiting small intestine absorption (malabsorption syndrome, resection of the small bowel, poorly controlled inflammatory bowel disease, etc.)