Brigatinib Plus Chemotherapy or Local Consolidation Therapy in ALK Positive Advanced Non-small Cell Lung Cancer (BrightStar-2)

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 (a) TKI naïve or (b) after/during 12 weeks of first line brigatinib treatment without disease progression or (c) after 4 weeks of first line alectinib, lorlatinib or ensartinib treatment without disease progression, those patients must be switched to brigatinib. Candidate for local consolidation therapy in the opinion of the treating physician. 5\. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 6. Males or females ≥ 18 years. Because no dosing or adverse event data are currently available on the use of brigatinib in combination with other agents in patients \<18 years of age, children are excluded from this study. 7\. Adequate organ function laboratory values, defined as: a. Absolute neutrophil count (ANC) ≥ 1.5 x 109/L or at least 1500/mm3 or at least 1.5 x 109/L b. Platelet count at least 75,000/mm3 or at least 75 x 109/L c. Hemoglobin (Hb) at least 9 g/dL (or 5.69 mmol/L) at baseline d. Serum creatinine ≤ 1.5 × ULN or ≥ 60 mL/minute for subjects with creatinine clearance levels \> 1.5 × the institutional ULN e. Serum total bilirubin less than or equal to ≤ 1.5 × ULN or direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 × ULN f. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN except for subjects with liver metastases for whom ALT and AST should be ≤ 5× ULN g. International Normalized Ratio (INR) or prothrombin time (PT) ≤ 1.5 × ULN unless subject is receiving anticoagulant therapy if PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants h. Activated PTT (aPTT) ≤ 1.5 × ULN unless subject is receiving anticoagulant therapy if 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 The effects of brigatinib on the developing human fetus are unknown. For this reason and because tyrosine kinase inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: 1. Postmenopausal (no menses in greater than or equal to 12 consecutive months). 2. History of hysterectomy or bilateral salpingo-oophorectomy. 3. Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). 4. History of bilateral tubal ligation or another surgical sterilization procedure. 5. Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 10\. Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: a. Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug, or b. Agree to completely abstain from heterosexual intercourse c. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of brigatinib administration. 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. 13\. Ability to understand and the willingness to sign a written informed consent document. 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 have had at least 2 years elapsed since the completion of radical treatment and the adjuvant therapy, if any, of the other primary malignancy. 2\. Previously received any prior TKI, including ALK-targeted TKIs. Note: on-going first line brigatinib, alectinib, lorlatinib and ensartinibuse as specified in the Inclusion criteria is allowed. 3\. Previously received more than 1 cycle of chemotherapy +/-immunotherapy for locally advanced or metastatic disease. 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\. Have uncontrolled hypertension. Patients with hypertension as defined by current standard of practice should be under treatment on study entry to control blood pressure. 10\. Received radiation therapy within 14 days before randomization except for stereotactic radiosurgery (SRS) or stereotactic body radiation therapy. 11\. Had major surgery within 30 days of enrollment. Minor surgical procedures, such as catheter placement or minimally invasive biopsies, are allowed. 12\. Have significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to the following: a) Myocardial infarction within 6 months before enrollment. b) Unstable angina within 6 months before enrollment. c) New York Heart Association Class III or IV heart failure within 6 months before enrollment. d) History of clinically significant atrial arrhythmia (including clinically significant bradyarrhythmia), as determined by the treating physician. e) Any history of clinically significant ventricular arrhythmia. 13\. Had a cerebrovascular accident within 6 months before first dose of study drug. 14\. Have an ongoing or active infection, including the requirement for intravenous antibiotics. 15\. Subjects should not receive other anti-cancer agents (e.g., chemotherapy, immunotherapy, biologic therapy, and/or hormone therapy other than for replacement or appetite stimulant) while on treatment in this study. 16\. History of allergic reactions attributed to compounds of similar chemical or biologic composition to brigatinib, carboplatin and pemetrexedor other agents used in study. 17\. Have a known history of human immunodeficiency virus (HIV) infection. Testing is not required in the absence of history. 18\. Pregnant women are excluded from this study because brigatinib is a tyrosine kinase inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with brigatinib, breastfeeding should be discontinued if the mother is treated with brigatinib. These potential risks may also apply to other agents used in this study.