Local Consolidative Therapy and Brigatinib in Treating Patients With Stage IV or Recurrent Non-small Cell Lung Cancer

Inclusion Criteria: 1. Histologically or cytologically confirmed diagnosis of stage IV NSCLC (or recurrent NSCLC not a candidate for definitive multimodality therapy) 2. Documented ALK re-arrangement as detected by: (1) FISH, (2) IHC, (3) tissue NGS, or (4) cfDNA NGS 3. Subjects can be enrolled as (1) TKI naïve or (2) after ≤ 8 weeks of first-line brigatinib treatment without disease progression. 4. Candidate for local consolidative therapy to at least one site of residual disease 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 6. Males or females aged at least 18 years. 7. Adequate organ function laboratory values, defined as: 1. Absolute neutrophil count (ANC) ≥ 1.5 x 109/L or at least 1500/mm3 or at least 1.5 x 109/L 2. Platelet count at least 75,000/mm3 or at least 75 x 109/L 3. Hemoglobin (Hb) at least 9 g/dL (or 5.69 mmol/L) at baseline 4. Serum creatinine ≤ 1.5 × ULN or ≥ 60 mL/minute for subjects with creatinine levels \> 1.5 × the institutional ULN 5. Serum total bilirubin less than or equal to ≤ 1.5 × ULN or direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 × ULN 6. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN except for subjects with liver mets for whom ALT and AST should be ≤ 5× ULN 7. International Normalized Ratio (INR) or prothrombin time (PT) ≤ 1.5 × ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants 8. Activated PTT (aPTT) ≤ 1.5 × ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulant 8. Female patients of childbearing potential must have a negative pregnancy test documented at time of screening. 9. Female patients who: 1. Are postmenopausal for at least 1 year before the screening visit, OR 2. Are surgically sterile, OR 3. If they are of childbearing potential, agree to use a highly effective method of contraception from the time of signing the informed consent through 4 months after the last dose of study drug, or agree to completely abstain from heterosexual intercourse 10. Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: 1. Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug, or 2. Agree to completely abstain from heterosexual intercourse 11. Have normal QT interval on screening ECG evaluation, defined as QT interval corrected (Fridericia) (QTcF) of ≤450 milliseconds (msec) in males or ≤470 msec in females. 12. Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol. Exclusion Criteria: 1. Have been diagnosed with another primary malignancy other than NSCLC, except for adequately treated non-melanoma skin cancer or cervical cancer in situ; definitively treated non-metastatic prostate cancer; or patients with another primary malignancy who are definitively relapse-free with at least 2 years elapsed since the diagnosis of the other primary malignancy. 2. Previously received any prior TKI, including ALK-targeted TKIs. Note: on-going first-line brigatinib use as specified in the Inclusion criteria is allowed. 3. Previously received more than 1 regimen of chemotherapy or immunotherapy for locally advanced or metastatic disease. Note that history of consolidative immunotherapy after concurrent chemoradiotherapy (for locally advanced disease) is allowed. 4. Symptomatic CNS metastasis. Asymptomatic CNS disease requiring increasing dose of corticosteroids within 7 days prior to study enrollment is also not permitted. 5. Have current spinal cord compression (symptomatic or asymptomatic and detected by radiographic imaging). Patients with leptomeningeal disease and without cord compression are allowed. 6. The presence of pulmonary interstitial disease, drug-related pneumonitis, or radiation pneumonitis at screening. 7. Have a known or suspected hypersensitivity to brigatinib or its excipients. 8. Have malabsorption syndrome or other gastrointestinal (GI) illness or condition that could affect oral absorption of the study drug. 9. Be pregnant, planning a pregnancy, or breastfeeding. 10. Have significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to: 1. Myocardial infarction (MI) within 6 months prior to the first dose of study drug 2. Unstable angina within 6 months prior to first dose of study drug 3. Decompensated congestive heart failure (CHF) within 6 months prior to first dose of study drug 4. History of clinically significant atrial arrhythmia (including clinically significant bradyarrhythmia), as determined by the treating physician 5. Any history of ventricular arrhythmia 6. Cerebrovascular accident or transient ischemic attack within 6 months prior to first dose of study drug 11. Have uncontrolled hypertension. Patients with hypertension should be under treatment on study entry to control blood pressure 12. Have an ongoing or active infection, including, but not limited to, the requirement for intravenous (IV) antibiotics. 13. Have a known history of human immunodeficiency virus (HIV) infection. Testing is not required in the absence of history. 14. Have any condition or illness that, in the opinion of the investigator, would compromise patient safety or interfere with the evaluation of the study drug.