Inclusion Criteria:

          1. Signed and dated written informed consent prior to any study specific procedures,
             sampling and analyses

          2. Documented active disease requiring treatment that is relapsed or refractory as
             determined by RECIST or clinically defined changes.

          3. Aged ≥18 yrs

          4. Eastern Cooperative Oncology Group (ECOG) performance status ≤1 without 2 levels of
             ECOG deterioration within 2 weeks (wks) of signing the ICF

          5. Life expectancy ≥12 wks

          6. Measurable or evaluable disease according to disease-specific tumor assessment
             criteria

          7. Adequate hepatic/renal function at screening:

               -  AST and ALT ≤2.5 x Upper Limit of Normal (ULN)

               -  Bilirubin ≤1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or is of
                  non-hepatic origin)

               -  Creatinine ≤1.5 x ULN and creatinine clearance (CrCl) ≥50 mL/min, measured or
                  calculated by Cockgroft-Gault method

          8. Adequate cardiac function demonstrated by left ventricular ejection fraction ˃50% on
             screening echocardiogram

          9. International normalized ratio ˂1.2 x ULN

         10. Lipase ≤1.5 x ULN and serum amylase ≤1.5 x ULN and no prior history of pancreatitis

         11. Patient agrees to the collection of formalin fixed paraffin embedded block or slides
             from archival diagnostic samples or a pre-treatment tumor biopsy

         12. Willing and able to participate in all required study evaluations and procedures
             including receiving IV administration of study drug and admission to the hospital,
             when required, for at least 24 hrs during administration of study drug

         13. Women should use adequate contraceptive measures, should not breast feed and should
             have a negative pregnancy test prior to start of dosing, or must have evidence of
             non-child-bearing potential by one of the following criteria at screening:

               -  Women ˂ 50 yrs would be considered postmenopausal if they have been amenorrhoeic
                  for the last 12 months following the cessation of exogenous hormonal treatments,
                  and have serum follicle-stimulating hormone and luteinizing hormone levels in the
                  postmenopausal range for the institution

               -  Documentation of irreversible surgical sterilization by hysterectomy, bilateral
                  oophorectomy or bilateral salpingectomy but not tubal ligation

         14. Men should be willing to use barrier contraception (i.e., condoms) and refrain from
             sperm donation during and after the conduct of the trial

        Inclusion Criteria for Arm A low risk of TLS (dose escalation):

          1. Patient has histologically or cytologically confirmed diagnosis or an advanced,
             unresectable and/or metastatic malignancy for which there are no treatment options
             available known to provide clinical benefit as follows: Solid tumor, Lymphoma that
             meets TLS low risk criteria, Multiple myeloma

          2. Adequate hematologic function independent of transfusion and growth factor support for
             ≥7 days before screening assessment. Solid tumors/lymphoma/multiple myeloma without
             bone marrow (BM) involvement:

               -  Absolute neutrophil count ≥1,000 cells/mm^3

               -  Hemoglobin ≥9.0 g/dL

               -  Platelet count ≥100,000 cells/mm^3, or ≥35,000 cells/mm^3 with BM involvement

        Inclusion Criteria for Arm B intermediate risk (IR) and high risk (HR) TLS (dose
        escalation):

          1. Patients with histologically confirmed, relapsed or refractory hematologic malignancy
             for which there are no treatment options available known to provide clinical benefit.
             Patients must be classified as IR or HR TLS.

          2. Adequate hematologic function independent of transfusion and growth factor support for
             ≥7 days before screening assessment

          3. For AML and CMML patients, WBC must be ˂15,000/µL. Treatment with hydroxyurea (HU)
             prior to study entry and during ramp-up to achieve this level is permitted, as long as
             there is ˃24 hrs between the start of study drug and use of HU.

          4. ALL/AML/MDS (IPSS-R intermediate/high/very high) and patients with BM involvement:

               -  No hematologic inclusion criteria

               -  Patient should be responsive to platelet transfusions to a minimum of 25,000
                  cells/mm^3 and having no history of thrombocytopenic bleeding

        Exclusion Criteria

          1. Patient has non-secretory myeloma

          2. Patient has idiopathic thrombocytopenic purpura

          3. Previously refractory to platelet transfusion within 1 yr

          4. Treatment with any of the following:

               -  Most recent radiotherapy ˂ 3 wks prior to first study treatment

               -  Treated with hormonal therapy, immunotherapy, chemotherapy or investigational
                  drugs within ≤21 days or 5 half-lives (whichever is shorter) from enrollment

               -  Major surgery (excluding placement of vascular access) ≤21 days from beginning of
                  the study drug or minor surgical procedures ≤7 days.

               -  Treatment with hematopoietic colony stimulating factors (e.g., filgrastim,
                  sargramostim) within 7 days of the first dose of study drug, or pegfilgrastim or
                  darbepoetin within 14 days of the first dose of study drug

               -  Patient has prescription/non-prescription drugs or other products known to be
                  sensitive BCRP, OCT2, OAT3, OAT P1B1, OAT P1B3, CYP2B6, CYP2C8, CYP2C9, or CYP
                  2D6 substrates, or reversible strong and moderate CYP3A inhibitors, which cannot
                  be discontinued within 5 half-lives of the drug before Day 1 of dosing and
                  withheld throughout the study until 14 days after the last dose of AZD0466

               -  Co-administration of CYP3A4 strong and moderate mechanism-based inhibitors or
                  inducers which cannot be discontinued within 5 half-lives plus 12 days of the
                  drug before Day 1 of dosing and withheld until 14 days after the last dose of
                  AZD0466

               -  Concurrent anti-coagulation therapy including aspirin which cannot be stopped

               -  History of medications with known risk of Torsades de Pointes (cardiac arrhythmia
                  due to drug-induced QTc prolongation) ≤5 half-lives before the start of treatment
                  and continuing until 5 half-lives after the last dose of AZD0466

               -  The use of live attenuated vaccines during the study through 30 days after the
                  last dose of study drug

          5. All toxicities from prior cancer therapy greater than NCI-CTCAE Grade (Gr) 1 will have
             returned to Gr1 at the time of enrollment with the exception of alopecia. Patients
             with Gr≤2 neuropathy are eligible.

          6. Previously untreated brain metastases. Patients who have received radiation or surgery
             for brain metastases are eligible if therapy was completed at least 21 days previously
             and there is no evidence of CNS disease progression or mild neurologic symptoms.

          7. Presence or history of CNS lymphoma, leptomeningeal disease or spinal cord compression

          8. Active infection including HIV, Hepatitis B, or Hepatitis C

          9. As judged by the Investigator, any evidence of severe or uncontrolled systemic
             diseases, (e.g., severe hepatic impairment, interstitial lung disease [bilateral,
             diffuse, parenchymal lung disease]); current unstable or uncompensated respiratory or
             cardiac conditions; uncontrolled hypertension; history of, or active, bleeding
             diatheses (e.g., hemophilia or von Willebrand disease); uncontrolled active systemic
             fungal, bacterial, viral, or other infection (exhibiting ongoing signs/symptoms
             related to the infection and without improvement, despite appropriate
             antibiotics/other treatment); or IV anti-infection treatment within 14 days before
             first dose of study drug

         10. Patients who have a high risk of developing renal dysfunction/renal involvement

         11. Undergone any of the following procedures or experienced any of the following
             conditions currently or in the preceding 6 months:

               -  Coronary artery bypass graft

               -  Angioplasty

               -  Vascular stent

               -  Myocardial infarction

               -  Angina pectoris

               -  Congestive heart failure (New York Heart Association Class ≥2)

               -  Ventricular arrhythmias requiring continuous therapy

               -  Supraventricular arrhythmias, including atrial fibrillation, which are
                  uncontrolled

               -  Hemorrhagic or thrombotic stroke, including transient ischemic attacks or any
                  other CNS bleeding

         12. Any of the following cardiac criteria:

               -  History of cardiomyopathy, myocarditis, or heart failure

               -  Mean resting corrected QT interval (QTcF) ≥470 msec obtained from 3 ECGs in the
                  absence of a cardiac pacemaker

               -  Any clinically important abnormalities in rhythm, conduction, or morphology of
                  resting ECG (e.g., complete left bundle branch block, third degree heart block,
                  intermittent or persistent bundle branch block, AV block II-II or clinically
                  significant sinus pause)

               -  Any factors that increase the risk of QTc prolongation or risk of arrhythmic
                  events such as heart failure, hypokalaemia, congenital long QT syndrome, or
                  family history of long QT syndrome or unexplained sudden death under 40 yrs of
                  age

         13. Abnormal ECHO at screening LVEF ≤50%

         14. History of hypersensitivity to polyethylene glycol (PEG), PEGylated products or drugs
             with a similar chemical structure or class to AZD0466 or other BH3 mimetic

         15. Lactating, breastfeeding, or positive pregnancy test

         16. Patient has a prior history of another life-threatening malignancy ≤2 yrs prior to
             first dose of study drug with the exception of:

               -  Malignancy treated with curative intent and with no evidence of active disease
                  present for more than 2 yrs before screening and felt to be at low risk of
                  recurrence by the treating physician

               -  Adequately treated lentigo malignant melanoma without current evidence of disease
                  or adequately controlled non-melanomatous skin cancer

               -  Adequately treated carcinoma in situ without current evidence of disease

         17. Psychological, familial, sociological, or geographical conditions that do not permit
             compliance with the protocol

         18. Judgement by the Investigator or Medical Monitor that the patient should not
             participate in the study if the patient is unlikely to comply with study procedures,
             restrictions, and requirements

        Exclusion criteria for Arm A low risk of TLS (dose escalation):

          1. Patients at IR or HR of developing TLS, including:

               -  T-cell, diffuse large B-cell, peripheral T-cell, transformed, and mantle cell
                  (blastoid variants) lymphoma patients with LDH ˃ULN

               -  Early and advanced stage Burkitt lymphoma or lymphoblastic lymphoma patients

               -  ALL, CLL, Richter's syndrome, AML, AML secondary, MDS, and chronic myelomonocytic
                  leukemia (CMML)

          2. Patients with a low risk of TLS that have significant renal dysfunction and/or renal
             involvement. Patients with CrCl ˂80 mL/min and/or who have higher tumor burden may be
             handled as TLS IR or HR patients.

        Exclusion criteria for Arm B IR and HR TLS (dose escalation):

          1. Patients with hematologic malignancies at HR of developing TLS are excluded from the
             first three cohorts. This includes:

               -  ALL patients with white blood cell (WBC) counts ≥15 x 10^9/L with no HU in last
                  24 hrs or with WBC counts ˂100 x 10^9/L accompanied by LDH ≥2 x ULN

               -  AML patients with WBC counts ≥100 x 10^9/L with no HU in the last 48 hrs

               -  Patients with acute Burkitt leukemia

          2. Patients with IR disease for TLS that also exhibits significant renal dysfunction,
             i.e., CrCl as calculated by Cockcroft-Gault method, if classified at investigator
             discretion as high-risk