This is a multicenter, open label, Phase 1 dose escalation study of TJ004309 in combination with standard dose atezolizumab in patients with advanced or metastatic cancer in patients who are refractory to or intolerant to all available therapy.

Inclusion Criteria:

1. Histologically confirmed advanced or metastatic cancer in patients who are refractory to or intolerant to all available therapy.
2. Measurable disease by iRECIST
3. Formalin fixed, paraffin-embedded (FFPE) tumor tissue that permits the preparation of 12 unstained slides of tumor sample- Biopsy must be excisional, incisional, or core. Needle aspiration is insufficient.
4. Age ≥ 18 years
5. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1
6. Resolution of all acute adverse events resulting from prior cancer therapies to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) Grade ≤ 1 or baseline (except alopecia or neuropathy)
7. Adequate organ function
8. Willingness and ability to consent for self to participate in study
9. Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests, and other study procedures

Exclusion Criteria:

1. Autoimmune disease requiring treatment within the past twelve months
2. Condition requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days prior to study treatment
3. History of or active interstitial lung disease
4. Prior T-cell or NK cell therapy
5. Current treatment on another therapeutic clinical trial
6. Receipt of systemic anticancer therapy, including investigational agents, within 28 days prior to study treatment
7. Major surgical procedure or significant traumatic injury within 4 weeks prior to study treatment, and must have fully recovered from any such procedure; and no date of surgery (if applicable) or anticipated need for a major surgical procedure planned within the next 6 months
8. Chest radiotherapy ≤ 28 days, wide field radiotherapy ≤ 28 days (defined as > 50% of volume of pelvic bones or equivalent), or limited field radiation for palliation ≤ 14 days prior to study treatment - such patients must have recovered adequately from any side effects of such therapy.
9. Hypertension defined as blood pressure (BP) systolic > 150 or diastolic > 90 mm Hg
10. Ascites or pericardial effusion that required intervention within 3 months prior to study treatment.
11. Brain involvement with cancer, spinal cord compression, or carcinomatous meningitis, or new evidence of brain or leptomeningeal disease, unless the lesion(s) have been radiated or resected, are considered fully treated and inactive, are asymptomatic, and no steroids have been administered for CNS disease over the 7 days prior to study treatment
12. Angina, myocardial infarction (MI), symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack TIA), arterial embolism, pulmonary embolism, percutaneous transluminal coronary angioplasty (PTCA), or coronary artery bypass grafting (CABG) within 6 months prior to study treatment
13. Thrombolytic use (except to maintain IV catheters) within 10 days prior study treatment
14. Known active viral or nonviral hepatitis or cirrhosis, except patients with Hepatitis C infection and undetectable virus following treatment are eligible.
15. Any active infection requiring systemic treatment
16. History of hemorrhage or hemoptysis (> ½ teaspoon bright red blood) within 3 months prior to study treatment
17. Known human immunodeficiency virus (HIV) unless CD4+ T cell count > 350 cells/μL with an undetectable viral load.
18. Pregnancy or breastfeeding - Female patients must be surgically sterile (i.e., ≥ 6 weeks following surgical bilateral oophorectomy with or without hysterectomy or tubal ligation) or be postmenopausal for at least one year, or must agree to use effective contraception during the study and for 5 months following last dose of TJ004309. All female patients of reproductive potential must have a negative pregnancy test (serum or urine) within 7 days prior to study treatment. Male patients must be surgically sterile or must agree to use effective contraception during the study and for 5 months following last dose of TJ004309.
19. Patients with any severe infection within 4 weeks prior to initiation of study treatment, including, but not limited to, hospitalization for complications of infections should not be enrolled in the trial. Patients who required IV antibiotics or were treated with antiviral medications within this 4 week period should be discussed with the TRACON prior to enrollment.
20. Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or may interfere with the interpretation of study results and, in the judgment of the Investigator, would make the patient inappropriate for this study