A Study of BNC105P Combined With Ibrutinib

Inclusion Criteria: * Patients who are \> 18 years of age, must have histologically or flow cytometry confirmed diagnosis of B-cell chronic lymphocytic leukemia/small lymphocytic lymphoma (B-CLL/SLL) according to NCI-WG 1996 guidelines. The malignant B cells must co-express CD5 with CD19 or CD20. Patients who lack CD23 expression on their leukemia cells should be examined for (and found NOT to have) either t(11;14) or cyclin D1 overexpression, to rule out mantle cell lymphoma. Patients with CLL who have progressed on prior ibrutinib therapy will be eligible. Patients with B-cell prolymphocytic leukemia and patients with Richter's transformation of CLL/SLL are NOT eligible. * Active disease meeting at least 1 of the IWCLL 2008 criteria for requiring treatment: i) A minimum of any one of the following constitutional symptoms: * Unintentional weight loss \>10% within the previous 6 months prior to screening. * Extreme fatigue (unable to work or perform usual activities). * Fevers of greater than 100.5 F for ≥2 weeks without evidence of infection. * Night sweats without evidence of infection. ii) Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia. iii) Massive (i.e., \>6 cm below the left costal margin), progressive or symptomatic splenomegaly. iv) Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy. v) Progressive lymphocytosis with an increase of \>50% over a 2-month period, or an anticipated doubling time of less than 6 months. vi) Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids. * Patients must have received at least one prior therapy for CLL comprised of the following: i) ≥1 regimen containing an anti-CD20 antibody (e.g., rituximab, obinutuzumab) administered for ≥ 2 doses ii) ≥1 regimen containing ≥1 cytotoxic agent (eg, bendamustine, fludarabine, chlorambucil, cyclophosphamide) administered for ≥ 2 cycles * Patients must have ECOG performance status ≤2. * Patients must have organ function as defined below: i) direct bilirubin ≤2 X institutional ULN (unless due to known Gilbert's syndrome or compensated hemolysis directly attributable to CLL) ii) AST or ALT less than 2.5 X institutional ULN iii) estimated CrCL using the Cockroft-Gault equation ≥50 mL/min (see formula in Appendix 2). iv) platelets ≥50,000/mm3 independent of transfusion support, with no active bleeding, and absolute neutrophil count ≥1000/mm3, unless due to disease involvement in the bone marrow. * Ability to understand and the willingness to sign a written informed consent document. * Women of childbearing potential must have a negative serum beta-human chorionic gonadotropin or urine pregnancy test at screening. * All patients of reproductive potential (heterosexually active men and women) must agree to a use of a barrier method of contraception and a second method of contraception and men must agree not to donate sperm during the study and for 4 weeks after receiving the last dose of study treatment. Exclusion Criteria * Prior therapeutic intervention with any of the following: * nitrosoureas or mitomycin C within 6 weeks; * therapeutic anticancer antibodies (including rituximab) within 4 weeks; * radio- or toxin-immunoconjugates within 10 weeks; * all other chemotherapy, radiation therapy within 3 weeks prior to initiation of therapy. * Inadequate recovery from adverse events related to prior therapy to grade ≤1 (excluding Grade 2 alopecia and neuropathy). * Chronic use of corticosteroids in excess of prednisone 20 mg/day or its equivalent. * Stem cell transplant recipients must have no evidence of active graft-versus-host disease. * Use of full dose, therapeutic anti-coagulation with warfarin. * Concomitant use of strong CYP inducers or inhibitors including nutraceutical preparations, e.g., grapefruit juice and St John's Wort * History prior malignancy except: * Malignancy treated with curative intent and no known active disease present for ≥ 2 years prior to initiation of therapy on current study; * adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease; * adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease; * asymptomatic prostate cancer managed with "watch and wait" strategy; * myelodysplastic syndrome which is clinically well controlled and no evidence of the cytogenetic abnormalities characteristic of myelodysplasia on the bone marrow at screening. * Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions). * Thrombotic events (pulmonary embolism; deep venous thrombosis) within 6 month prior to start of therapy. * History of Human Immunodeficiency Virus (HIV) infection or active hepatitis B or C. Intravenous immunoglobulin (IVIG) can cause a false positive hepatitis B serology. If patients receiving routine IVIG have core antibody or surface antigen positivity without evidence of active viremia (negative hepatitis B DNA) they may still participate in the study, but should have hepatitis serologies and hepatitis B DNA monitored periodically by the treating physician. * Patients with the following cardiovascular abnormalities: * Corrected QT interval (QTc) \>500 msec within 7 days prior to registration for protocol therapy. NOTE: if QTc is \>450 and ≤500 msec, subject to local cardiology review and approval, the patient may be enrolled if the QTc elevation is deemed clinically insignificant. * Acute cardiovascular events within 6 months prior to C1D1: stroke (transient ischemic attack permitted), acute coronary syndrome, peripheral arterial obstruction, clinically significant arrhythmias (e.g., such as paroxysmal atrial fibrillation/atrial flutter, sick sinus syndrome, second or third degree atrio-ventricular blockade). A cardiology consultation may be obtained to clarify clinical significance. * Clinical cardiac heart failure of New York Heart Association Class III or IV or left ventricular ejection fraction (LVEF) \<50% as assessed by echocardiogram at screening. * Major surgery (requiring general anesthesia) within 30 days prior to initiation of therapy. * Inability to swallow and retain an oral medication. Patients with clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting or any other condition that will interfere significantly with the absorption of ibrutinib are excluded. * Any condition for which participation in the study is judged by the Investigator to be detrimental to the patient with inter-current illness including, but not limited to an uncontrolled active infection; unstable angina pectoris; uncontrolled cardiac arrhythmia or psychiatric/social situations that would jeopardize compliance with study requirements.