The purpose of this study is to evaluate the safety, tolerability and clinical activity of RO6870810 in combination with venetoclax and when co-administered with rituximab in participants with relapse/refractory (R/R) diffuse large B-cell lymphoma (DLBCL) and/or high-grade B-cell lymphoma with myelocytomatosis oncogene (MYC) and/or B-cell lymphoma 2 (BCL2) and/or B-cell lymphoma 6 (BCL6) gene rearrangements (HGBL-DH/TH).

Inclusion Criteria

• Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2.
• Life expectancy >3 months as per investigator's assessment.
• Part 1 and Part 2 Group 1: Participantts with diffuse large B-cell lymphoma (DLBCL) relapsed or refractory to ≥ 1 course of chemotherapy including an anti-CD20 monoclonal antibody, and not eligible for autologous stem cell transplantation (ASCT) (including due to chemorefractory disease). Participants with transformed FL are eligible, provided DLBCL or HGBL-DH/TH histology is biopsy-confirmed prior to study entry and a treatment regimen as described above has been administered. The Sponsor retains the option to limit the number of participants enrolled with transformed FL.

Part 2, Group 2: Patients identified with DE-DLBCL (expression MYC ≥40%, BCL2 > 50%) and or HGBL-DH/TH, relapsed or refractory to >= 1 course of chemotherapy including an anti-CD20 monoclonal antibody, and not eligible for ASCT (including due to chemorefractory disease). Patients with transformed follicular lymphoma (FL) are eligible, provided DE-DLBCL and/or HGBL-DH/TH histology is biopsy-confirmed prior to study entry and a treatment regimen as described above has been administered. The Sponsor retains the option to limit the number of participants enrolled with transformed FL.

• Part 1 and Part 2: Willing to provide the protocol specified tumor biopsy(ies): at screening a fresh biopsy (if no archival biopsy tissue of less than 3 months prior to treatment and without intercurrent treatment is available); Part 2: Willing to provide an additional biopsy on Cycle 2 Day 15 (+ 2 days).

• Acceptable liver function, as specified below:

  • Total bilirubin ≤ 2 times upper limit of normal (ULN). (Participants with known Gilbert's disease who has serum bilirubin ≤ 3 × ULN may be enrolled).
  • Aspartate transaminase (AST; SGOT), alanine transaminase (ALT; SGPT) ≤ 2.5 × ULN, (or ≤ 5 × ULN if tumor involvement (liver) is present).
  • Gamma-glutamyl transferase (GGT) alkaline phosphatase ≤ 2.5 × ULN.

• Acceptable renal function, as specified below:

  • Creatinine clearance (CrCl) calculated by Cockroft-Gault formula of ≥ 60 mL/min.

• Acceptable hematologic status (growth factors cannot be used within the previous 7 days), as specified below:

  • Absolute neutrophil count (ANC) ≥ 1000 cells/μL
  • Hemoglobin ≥ 9 g/dL
  • Platelet count ≥ 75,000 (platelets/μL)

• Uncontrolled symptomatic hypercalcemia.

• Acceptable coagulation status, as specified below:

  • Prothrombin time (PT) and partial thromboplastin time (PTT) ≤ 1.2 × ULN (unless receiving anticoagulation therapy, if receiving anticoagulation therapy, eligibility will be based upon international normalized ratio [INR]).
  • INR ≤ 1.6 (unless receiving anticoagulation therapy).
  • If receiving warfarin: INR ≤ 3.0 and no active bleeding (i.e., no bleeding within 14 days prior to first dose of study therapy).

• Acceptable method of contraception

Exclusion Criteria

• Current central nervous system (CNS) lymphoma or leptomeningeal infiltration.

• New York Heart Association (NYHA) Class III or IV cardiac disease, myocardial infarction, within the past 6 months, unstable arrhythmia, or known pericardial disease.

• Fredericia-corrected QT interval (QTcF) >470 msec (female) or >450 msec (male), or history of congenital long QT syndrome.

• Any electrocardiogram (ECG) abnormality, which in the opinion of the Investigator would preclude safe participation in the study.

• Active, uncontrolled bacterial, viral, or fungal infections, within 7 days of study entry requiring systemic therapy.

• Clinically important respiratory impairment

• Grade ≥ 3 sensory or motor neuropathy.

• Any Grade >1 (according to the NCI CTCAE 4.03) adverse reaction unresolved from previous treatments and not readily managed and controlled with supportive care.

• Serious non-malignant disease that could compromise protocol objectives in the opinion of the Investigator and/or the Sponsor.

• History of progressive multifocal leukoencephalopathy (PML).

• History of other malignancy within 2 years prior to screening, except for ductal carcinoma in situ not requiring chemotherapy, appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, low-grade, localized prostate cancer (Gleason score ≤ 7) not requiring treatment or appropriately treated Stage I uterine cancer.

• Completion of ASCT within 100 days prior to Day 1 of Cycle1.

• Prior standard or investigational anti-cancer therapy, as specified below:

  • Radio-immunoconjugate 4 weeks or 5 half-lives, whichever is longer prior to Day 1 of Cycle 1.
  • Monoclonal antibody or antibody-drug conjugate (ADC) therapy within 3 weeks prior to Day 1 of Cycle 1.
  • Radiotherapy, chemotherapy, or targeted small-molecule therapy within 2 weeks prior to Day 1 of Cycle 1.
  • CAR T-cell therapy 30 days prior to Day 1 of Cycle 1.

• History of major solid organ transplant (i.e., heart, lungs, liver and kidney).

• History of an allogeneic bone marrow transplant.

• Major surgical procedure within 28 days prior to Day 1 of Cycle 1.

• Treatment with systemic corticosteroids ≥ 20 mg/day prednisone or equivalent, for non-lymphoma treatment reasons. For lower acceptable doses, documentation of a stable dose for at least 4 weeks prior to Day 1 of Cycle 1 is required.

  18. Treatment with strong to moderate CYP3A inhibitors or moderate CYP3A inducers within 7 days prior to the first dose of study treatment.

• Treatment with strong CYP3A inducers within 14 days prior to the first dose of study treatment of RO6870810/venetoclax.

• Consumption of grapefruits, grapefruit products, Seville oranges (including marmalade that contains Seville oranges), or star fruit within 3 days prior to the first dose of venetoclax.

• Participants who are currently receiving any other investigational agent ((other than anti-cancer therapy as specified in exclusion criteria number 13) or have received an investigational agent within 30 days or 5 half-lives prior to Day 1 of Cycle 1, whichever is longer.

• Prior treatment with small molecule bromodomain and extra terminal (BET) family inhibitor.

• Known to be human immunodeficiency virus (HIV) positive.

• Presence of positive test results for hepatitis B surface antigen (HBsAg) or hepatitis C antibodies (HcAb) (for participants receiving regimen including rituximab)

• Pregnant or breastfeeding female.

• Significant allergy to a biological pharmaceutical therapy that, in the opinion of the Investigator, poses an increased risk to the participant.

• Uncontrolled cancer pain. Participants requiring pain medication must be on a stable regimen at study entry. Symptomatic lesions amenable to palliative radiotherapy should be treated prior to enrollment.

• History of severe allergic or anaphylactic reaction to humanized or murine monoclonal antibodies (for participants receiving regimen including rituximab).

• Known sensitivity or allergy to murine products or any component of RO6870810, venetoclax, or rituximab.