Mosunetuzumab for CLL MRD Clearance

Key Inclusion Criteria: * Meet 2018 iwCLL guidelines for the diagnosis of CLL or SLL * Recent completion of treatment or ongoing treatment for CLL/SLL as follows: * BTKi arm: On continuous BTKi therapy for \> 12 months, including \> 2 months at a stable dose. * BTKis include ibrutinib, acalabrutinib, zanubrutinib and pirtobrutinib. * The BTKi is the first- or second-line therapy for CLL. * BCL2i arm: Completed BCL2i-based therapy \< 12 months of enrollment. * BCL2i-based therapy must be the most recent CLL therapy prior to enrollment. * BCL2i must have been given for at least 6 months for patients who were intolerant to a BCL2i and stopped the treatment without disease progression. For all others, at least 12 cycles of BCL2i therapy are required. * BCL2i-based therapy should have been given as first- or second-line therapy for CLL. * BCL2i-based regimens include venetoclax plus obinutuzumab (VO) or rituximab (VR), and the combination of a BTKi + a BCL2i +/- anti- CD20mAb. * If BCL2i was continued after the combination, the subject is not eligible. * Detectable minimal residual disease (MRD) of ≥10e-4 in peripheral blood (PB) or bone marrow (BM) based on an NGS-based assay. * Age ≥ 18 years * ECOG performance status ≤ 2 * Adequate organ and bone marrow function as defined by the study protocol. * Women of child-bearing potential must agree to remain abstinent or use highly effective contraception during the treatment period and for at least 3 months after the last dose of study therapy and tocilizumab. * Men with female sexual partners of childbearing potential should agree to remain abstinent or use contraceptive measures which include a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 1 month after the last dose of study therapy and 2 months after the last dose of tocilizumab. Men should refrain from donating sperm during the same period. Women should not donate oocytes. 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. * Ability to take oral medications. * Ability to understand and the willingness to sign a written informed consent document. Key Exclusion Criteria: * Bulky disease with any lymph node \> 5cm or absolute lymphocyte count \> 100,000/microliter. * Clinical progression of CLL at the time of enrollment. * Prior treatment with chimeric antigen receptor T-cell therapy within 30 days of starting study therapy, or radioimmunotherapy within 12 weeks of starting study therapy. * History of solid organ or allogeneic stem cell transplantation. * Ongoing significant toxicity (Grade 3 or higher adverse events) from prior BCL2i- or BTKi- -based therapy at the time of enrollment. * Known or suspected Richter's transformation or known CNS involvement of CLL. * History of bleeding disorders (e.g. von Willebrand's disease, hemophilia). * Current or past history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease. * Significant cardiovascular disease such as uncontrolled arrhythmi, class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification, ejection fraction \< 40% by any methods in the 12 months of enrollment, unstable angina or acute coronary syndrome including myocardial infarction within 6 months of enrollment. * Patients with significant pulmonary disease such as uncontrolled obstructive pulmonary disease, history of bronchospasm, uncontrolled idiopathic, autoimmune, or drug-induced interstitial lung disease, or uncontrolled drug induced or auto-immune pneumonitis * Clinically significant history of liver disease, including viral or other hepatitis, or cirrhosis * For patients with history of other malignancies with life expectancy of \< 2 years. * Receiving any other investigational agents. * Concurrent systemic immunosuppression (e.g. azathioprine, methotrexate, cyclosporine, tacrolimus, anti-TNF agents, anti-CD20 monoclonal antibody) within 30 days of starting study therapy or administration of \> 20 mg of prednisone or equivalent daily within 14 days of study therapy. * Vaccinated with live vaccine within 4 weeks of starting study therapy. * Major surgery within 4 weeks of starting study therapy. If a subject had major surgery greater than 4 weeks prior to the first dose, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study therapy. * Ongoing or recent infection (e.g. bacterial, viral, fungal, parasitic, or other infection) requiring intravenous antimicrobials within 4 weeks of starting study therapy. Prophylactic antibiotics are allowed if there is no evidence of active infection and the antibiotics is not included on the list of the prohibited medications. * Known or suspected history of hemophagocytic lymphohistiocytosis. * Known hypersensitivity to biopharmaceuticals produced in CHO cells or any component of the mosunetuzumab. * Concurrent treatment with warfarin or other vitamin K antagonists for anticoagulation. * Patients who have tested positive for HIV are excluded due to potential drug-drug interactions between anti-retroviral medications and pirtobrutinib and risk of opportunistic infections with both HIV and irreversible BTK inhibitors. For patients with unknown HIV status, HIV testing will be performed at Screening and result should be negative for enrollment. * Active hepatitis B virus or hepatitis C virus infection * History of progressive multifocal leukoencephalopathy. * Positive SARS-CoV-2 test within 7 days prior to enrollment. * Pregnancy, lactation or plan to breastfeed during the study or within 6 months of the last dose of study treatment. * Active uncontrolled autoimmune disease. * Significant co-morbid condition or disease which in the judgement of the Principal Investigator would place the patient at undue risk or interfere with the study.