Phase I Master Protocol of Novel Combination Therapy for Patients With Relapsed or Refractory Aggressive B-Cell Lymphoma

Inclusion Criteria: * Patients with histologic diagnosis for one of the following histologies according to the World Health Organization: documented at initial diagnosis or at relapse: * Diffuse large cell lymphoma, B-cell (includes primary mediastinal B-cell lymphoma, T-cell rich B-cell lymphoma); * Previous indolent lymphoma (follicular lymphoma, marginal zone lymphoma, including extranodal MALT lymphoma, lymphoplasmacytoid lymphoma) with transformation to diffuse large B-cell lymphoma at most recent relapse (biopsy proof of transformation is mandatory). * Patients with de novo aggressive B-cell lymphoma must have relapsed or progressed, or have biopsy-proven refractory disease, after one prior line of therapy (R-CHOP chemotherapy or equivalent). R-CHOP chemotherapy equivalents include R-CEOP, dose-adjusted EPOCH-R, CODOX-M/IVAC-R, and other combination regimens including a CD20 monoclonal antibody, alkylating agent and anthracycline. * Patients with histological transformation from low grade lymphoma may have had up to 3 prior treatment regimens. Patients with transformed low grade lymphoma treated with a non-anthracycline regimen may be enrolled at investigator discretion. * Patient must be considered fit for intensive chemotherapy and ASCT, and an appropriate candidate to receive second-line salvage chemotherapy and ASCT. Individuals older than 65 years of age are not recommended for this study. * Clinically and / or radiologically measurable disease (1 site dimensionally measurable). Measurements / evaluations must be done within 28 days prior to enrollment using the RECIL and Lugano criteria. * Age ≥ 16 years. (Note that the lower age limit at each centre will be determined by that centre's policy regarding the age at which an individual may sign his or her own consent.) * ECOG performance status 0, 1, 2 or 3. * Life expectancy of ≥ 90 days (3 months). * Laboratory Requirements: (must be done within 14 days of enrollment) * Absolute Neutrophil ≥ 1.0 x 10\^9/L (independent of growth factor support) * Platelets ≥ 100 x 10\^9/L (50 x 10\^9/L if bone marrow involvement by lymphoma, independent of transfusion support) * AST and ALT ≤ 3x ULN * Serum total bilirubin≤ 1.5x ULN (≤ 5x ULN if Gilberts Disease) * Serum Creatinine ≤ 1.5x ULN (or estimated GFR of ≥ 45 mL/min/1.73 m2 using Cockcroft Gault formula) * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to enrolment in the trial to document their willingness to participate. * Patients must be accessible for treatment and follow up. Patients enrolled on this trial must be treated and followed at the participating centre. This implies there must be reasonable geographical limits (for example: 1 ½ hours driving distance) placed on patients being considered for this trial. * In accordance with CCTG policy, protocol treatment is to begin within 5 working days of patient enrollment. * Women of childbearing potential who are sexually active must have agreed to use a highly effective contraceptive method during treatment and for 12 months after the end of treatment. Men must not father a baby or donate sperm while taking study treatment, and for 24 months after the last dose. Exclusion Criteria: * Patients concurrently receiving any other anti-cancer therapy (cytotoxic, biologic, radiation, or hormonal other than for replacement) except for medications that are prescribed for supportive care but may potentially have an anti-cancer effect. • Systemic therapy (cytotoxics, targeted agents and investigational drugs): patients must have recovered from all reversible toxicity related to prior treatment and have adequate washout prior to enrollment with the longest of: * Five half-lifes * Two weeks * Standard cycle length of prior regimen * Biologic agents e.g. monoclonal antibodies: not permitted within 28 days prior to enrollment. * Steroids: avoidance of steroids with anti-neoplastic intent in 7 days prior to study drug is preferred. However, if clinically required, it can be administered at investigator discretion (prednisone 40 mg for 4 days maximum, or equivalent) and must be captured on the electronic case report form. * Radiation: not permitted within 28 days prior to enrollment. * Active and uncontrolled central nervous system involvement, meningeal or parenchymal. Patients with CNS disease at initial presentation, and who are in a CNS CR at the time of relapse, are eligible. MRI scanning and / or lumbar puncture should be performed if there is clinical suspicion of active CNS disease. * Known history of human immunodeficiency virus (HIV), active Hepatitis C virus infection, active Hepatitis B virus infection or any uncontrolled active systemic infection. Patients with Hepatitis B serology suggestive of infection are eligible if they are HBV DNA negative and concurrently treated with anti-viral therapy. Patients with a history of hepatitis C who have eradicated the virus are eligible. * Patients who have been vaccinated with live, attenuated vaccines within 4 weeks of enrollment. * Patients with clinically significant pre-existing cardiac conditions, including uncontrolled or symptomatic angina, uncontrolled atrial or ventricular arrhythmias, or symptomatic congestive heart failure. * Patients with known left ventricular ejection fraction (LVEF) \< 40%. * Patients with stroke (including TIA) or acute myocardial infarction within three months prior to enrollment. * Patients with acute gastrointestinal bleeding within one month prior to enrollment. * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. However, patients on active anticancer therapy for other advanced or metastatic malignancies are not eligible, as this is a phase I study identifying a RP2D of a single agent and there is the potential for drug-drug interactions. Consult CCTG for patients who are on adjuvant therapies after curative surgery or in instances where it is felt the patient may be eligible (for example, TCC bladder receiving local therapies or CLL not requiring active therapy). * Pregnant or lactating females, or women of childbearing potential not willing to use an adequate method of birth control for the duration of the study. * Patients are not eligible if they have a known hypersensitivity to the study drugs or their components. * Patients with any other clinically significant medical condition which, in the opinion of the treating physician, makes it undesirable for the patient to participate in the study or which could jeopardize compliance with study requirements including, but not limited to: ongoing or active infection, significant uncontrolled hypertension, or severe psychiatric illness/social situations.