Inclusion Criteria:
* Age ≥ 18 years at the time of signing the informed consent form.
* Have a life expectancy (in the opinion of the investigator) of at least 12 weeks.
* Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%).
* History of previously treated MCL meeting the following criteria: Relapsed after or failed to respond to at least one prior line of systemic therapy including anti-CD20 monoclonal antibody and alkylator-containing chemotherapy.
* At least one bi-dimensionally measurable nodal lesion ( \> 1.5 cm in its largest dimension by PET/CT scan), or at least one bi-dimensionally measurable extranodal lesion ( \> 1.0 cm in its largest dimension by PET/CT scan) and FDG-avid.
* Availability of leftover tissue from the time of progression for pathology confirmation and correlative studies. Note: Formalin fixed paraffin embedded blocks are preferred. If blocks are not available, 12-15 slides containing unstained, serial sections are acceptable.
* Hemoglobin ≥ 9 g/dL (Independent of transfusions and within 7 days prior to screening assessment).
* Absolute neutrophil count \>= 1.0 x 10\^9/L (Independent of growth factor support and within 7 days prior to screening assessment).
* Platelets ≥ 75 x 10\^9/L or \>= 50 x 10\^9/L if due to bone marrow involvement (Independent of transfusions and within 7 days prior to screening assessment, and independent of growth factor support and within 7 days prior to screening assessment). If the patient is cytopenic there should be no evidence of myelodysplasia orhypoplastic bone marrow.
* Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (or ≤ 3 x ULN for participants with Gilbert syndrome, or \<= 3 x ULN if due to underlying lymphoma).
* Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase (SGOT)) \<= 2.5 X institutional upper limit of normal.
* Alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase (SGPT)) \<= 2.5 X institutional upper limit of normal.
* Creatinine clearance \>= 50 mL/min (by Cockcroft-Gault formula).
* Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) \<= 1.5 x ULN.
* Prothrombin (PT) or (international normalized ratio (INR) \<= 1.5 x ULN.
* In women of childbearing potential, negative serum pregnancy test within 7 days prior to study treatment and either abstinence or use of highly effective contraception methods from the time of screening for at least 18 months after pre-treatment with obinutuzumab, 2 months after the final dose of glofitamab, 1 month after last dose of pirtobrutinib, 3 months after the final dose of tocilizumab (if applicable), whichever is longer. Women of childbearing potential should not donate oocytes for 1 month after last dose of pirtobrutinib.
* For men: agreement to remain abstinent or use contraceptive measures and agreement to refrain from donating sperm, with female partners of childbearing potential or pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 3 months after pre-treatment with obinutuzumab, 2 months after the final dose of glofitamab, 28 days after last dose of pirtobrutinib, 3 months after the final dose of tocilizumab (if applicable), whichever is longer.
* Willing and capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in the protocol.
* Participants with prior treatment-related adverse events (AEs) must have recovered to grade \<= 1 with the exception of alopecia and grade 2 peripheral neuropathy.
* Participants must be able to swallow oral medications.
* Participants with positive hepatitis B core antibody (anti-HBc) and negative hepatitis B surface antigen (HBsAg) require a negative hepatitis B polymerase chain reaction (PCR) evaluation before initiating study treatment on cycle 1 day 1. Participants with positive anti-HBc antibody are required to receive prophylactic antiviral therapy with lamivudine, tenofovir, or entecavir for the duration of treatment and for at least 6 months following the end of study treatment. Hepatitis B PCR should be repeated as clinically indicated.
* Individuals with a history of hepatitis C virus (HCV) infection must have been treated and cured. For individuals with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.
Exclusion Criteria:
* Pregnant, or intention of becoming pregnant during the study or within 18 months after treatment with obinutuzumab or 2 months after the last dose of glofitamab, or 3 months after treatment with tocilizumab, whichever is longer; and 1 month after the last dose of pirtobrutinib.
* Participants should avoid chest-feeding until at least 1 week after discontinuing pirtobrutinib.
* Have received the following treatments/procedures prior to study entry:
* Participants who experienced a major bleeding event or grade ≥ 3 arrhythmia on prior treatment with a BTK inhibitor. NOTE: Major bleeding is defined as bleeding having one or more of the following features: potentially life-threatening bleeding with signs or symptoms of hemodynamic compromise; bleeding associated with a decrease in the hemoglobin level of at least 2g per deciliter; or bleeding in a critical area or organ (e.g., retroperitoneal, intraarticular, pericardial, epidural, or intracranial bleeding or intramuscular bleeding with compartment syndrome)
* Participants who discontinued a covalent BTK inhibitor due to disease progression or relapse. NOTE: Participants who discontinued covalent BTK inhibitor therapy due to intolerance will not be excluded. Covalent BTK inhibitor intolerance is defined as:
* Any grade 3 or higher non-hematologic toxicity, except a major bleeding event or grade \>= 3 arrhythmia which are exclusion criteria
* Any grade 1 or higher non-hematologic toxicity that lasted longer than 7 days or recurred
* Any grade 4 hematologic toxicity
* Neutropenic fever
* Discontinuation due to drug interaction/expected toxicity with resolution of prior covalent BTK inhibitor-related toxicities
* Any CD20/CD3-directed bispecific antibodies for treatment of lymphoma
* Allogeneic stem cell transplant (SCT) within 6 months or on active immunosuppression or active graft versus host disease (GVHD)
* Solid organ transplantation
* Have received the following treatments/procedures prior to study entry whether investigational or approved, within the respective time periods prior to initiation of study treatment:
* Radiotherapy within 2 weeks prior to the first dose of study treatment. Note: If participants have received radiotherapy within 4 weeks prior to the first study treatment administration, participants must have at least one measurable lesion outside of the radiation field
* Autologous SCT within 90 days prior to first study treatment
* Chimeric antigen receptor (CAR) T-cell therapy within 60 days before first study treatment or if ongoing toxicity ≥ grade 2
* Use of monoclonal antibodies or antibody-drug conjugates within 4 weeks prior to first study treatment
* Use of radioimmunoconjugates within 12 weeks prior to first study treatment
* Systemic immunosuppressive medications (including, but not limited to, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents) within 2 weeks or five half-lives (whichever is shorter) prior to first dose of study treatment. Note: Systemic corticosteroid treatment . 10 mg/day prednisone or equivalent and inhaled corticosteroids are permitted. Administration of acute, low-dose, systemic immunosuppressant medications (e.g., single dose of dexamethasone for nausea or B symptoms) is permitted. The use of mineralocorticoids for management of orthostatic hypotension and corticosteroids for management of adrenal insufficiency is permitted
* Live, attenuated vaccine within 4 weeks before first dose of study treatment, or in whom it is anticipated that such a live attenuated vaccine will be required during the study period or within 5 months after the final dose of study treatment
* Evidence of active central nervous system (CNS) lymphoma or leptomeningeal infiltration
* Current or history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease. Note: Participants with a history of stroke who have not experienced a stroke or transient ischemic attack within the past 2 years and have no residual neurologic deficits, as judged by the investigator, are allowed
* Active second malignancy unless the patient is in remission and has a life expectancy \> 2 years.
* Major surgical procedure (under general anesthesia) within 30 days of day 1 of protocol therapy. Note: If a patient had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug
* History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibody therapy (or recombinant antibody-related fusion proteins).
* History of autoimmune disease, including but not limited to myocarditis, pneumonitis, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Guillain- Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis Note: Participants with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone, participants with a history of disease-related immune thrombocytopenic purpura or autoimmune hemolytic anemia, and participants with a history of type I diabetes mellitus who are well controlled (defined as a screening glycosylated hemoglobin (hemoglobin A1c) ≤ 8% and no urinary ketoacidosis) may be eligible for this study. Investigators should consult the sponsor-investigator.
* Significant or extensive history of cardiovascular disease such as New York Heart Association class III or IV or objective class C or D cardiac disease, myocardial infarction within the previous 6 months, unstable arrhythmia, or unstable angina or acute coronary syndrome within the past 2 months prior to start of study treatment (cycle 1 day 1 (C1D1)), uncontrolled or symptomatic arrhythmias, and/or documented left ventricular ejection fraction (LVEF) by any method of ≤ 40% in the 12 months prior to start of study treatment (C1D1)
* Prolongation of the QTc for heart rate using Fridericia's Formula (QTcF) \> 470 msec. Note: Correction of QTc for underlying bundle branch block is permissible.
* Significant pulmonary disease that is expected to interfere with therapy.
* History of confirmed progressive multifocal leukoencephalopathy (PML).
* Known active infection (including Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)), or reactivation of a latent infection, whether bacterial, viral (including, but not limited to, Epstein-Barr virus (EBV), cytomegalovirus (CMV), hepatitis B and hepatitis C), fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization within 4 weeks (relating to the completion of the course of antibiotics) prior to first study treatment administration.
* Participants requiring therapeutic anticoagulation with warfarin or another vitamin K antagonist.
* Known or suspected history of hemophagocytic lymphohistiocytosis (HLH).
* Participants who have tested positive for human immunodeficiency virus (HIV) are excluded due to risk of opportunistic infections with both HIV and BTK inhibitors. For participants with unknown HIV status, HIV testing will be performed at screening and result must be negative for enrollment.
* Participants with a history of bleeding diathesis.
* Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal (GI) absorption of the study drug.
* A known hypersensitivity to any of the excipients of pirtobrutinib or to any of the intended study medications.
* Participants requiring ongoing therapy with strong Cytochrome P450, family 3, subfamily A (CYP3A) inhibitors or inducers will be excluded. For participants who are able to discontinue therapy with a strong CYP3A modulator, a washout period of at least 5 half-lives is required before beginning study treatment.
