A Phase IB/II Study of Alectinib Combined With Cobimetinib in Advanced ALK-Rearranged (ALK+) NSCLC

Inclusion Criteria: * Ability to understand and the willingness to sign a written informed consent document. * Age ≥ 18 years. * Histologically or cytologically confirmed diagnosis of metastatic NSCLC (Stage IV, AJCC v7.0) that carries an ALK rearrangement, as determined by the Food and Drug Administration (FDA)-approved fluorescence in-situ hybridization (FISH) test, using Vysis® ALK Break apart FISH Probe, or the Ventana® immunohistochemistry (IHC) test. Diagnosis using next generation sequencing (NGS) via a local diagnostic test will be accepted for enrollment but will need to be confirmed with either FISH or IHC. * For the expansion cohort: Patients must have had disease progression on alectinib (including patients who received alectinib as first-line treatment). Subsequent anti-neoplastic therapy (including other ALK inhibitors or chemotherapy) after progression on alectinib is not permitted. Note: patients in the dose-finding portion of the study may have received other anti-neoplastic therapy after progression on alectinib. * At least one measurable lesion as defined by RECIST version 1.1. Previously irradiated lesions are not measurable unless the lesion has demonstrated clear progression after radiation. * Eastern Cooperative Group (ECOG) performance status ≤ 2 for patients treated in the expansion phase. ECOG PS ≤ 1 is required for participants in the dose-finding portion of the study. * Life expectancy of greater than 12 weeks * Patient willingness and disease accessible to pre-treatment, on-treatment tumor, and progression biopsies (core biopsies). A cell block from a pleural effusion may be substituted for a core biopsy. * Able to swallow and retain orally administered medication. Does not have any clinically significant gastrointestinal abnormalities, such as malabsorption syndrome or major resection of the stomach or small bowel that may alter absorption of the medication. * For participants in the dose-finding phase, a minimum washout period of at least 5 half-lives between the last dose of tyrosine kinase inhibitor (TKI) therapy and the first dose of study treatment is required. For patients on crizotinib, a 7 day washout is sufficient. A shorter washout period may be considered in the event of disease flare, after discussion with the Sponsor. No washout is required if the most recent anti-neoplastic therapy is alectinib. * Patients must have recovered from treatment toxicities to ≤ Grade 1 or to their pretreatment levels except for adverse events (AEs) that in the investigator's judgment do not constitute a safety risk for the patient. * Patients can either be chemotherapy-naive or have received platinum-based chemotherapy for locally advanced or metastatic disease. Acute effects of therapy must have resolved to baseline severity or to CTCAE grade ≤1 except for AEs that in the investigator's judgment do not constitute a safety risk for the patient. Patients who have received prior treatment with checkpoint inhibitors are eligible. * Recovery from effects of any major surgery or significant traumatic injury at least 28 days before the first dose of study treatment * For all women of childbearing potential, a negative pregnancy test must be obtained at the baseline visit before starting study treatment. For women who are not postmenopausal (≥ 12 months of non-therapy-induced amenorrhea) or surgically sterile (absence of ovaries and/or uterus): agreement to remain abstinent or use two adequate methods of contraception, including at least one method with a failure rate of \< 1% per year, during the treatment period and for at least 90 days after the last dose of study drug. * Abstinence is only acceptable if it is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not acceptable methods of contraception. * Examples of contraceptive methods with a failure rate of \< 1% per year include tubal ligation, male sterilization, hormonal implants, established, proper use of combined oral or injected hormonal contraceptives, and certain intrauterine devices. Alternatively, two methods (e.g., two barrier methods such as a condom and a cervical cap) may be combined to achieve a failure rate of \<1% per year. Barrier methods must always be supplemented with the use of a spermicide. * For men: agreement to remain abstinent or use a barrier method of contraception (e.g., condom) during the treatment period and for at least 90 days after the last dose of study drug and agreement to refrain from donating sperm during this same period * Men with a pregnant partner must agree to remain abstinent or use a condom for the duration of the pregnancy. * Abstinence is only acceptable if it is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. * Patients with untreated, controlled asymptomatic central nervous system (CNS) lesions are allowed in this trial as long as the CNS is not a site of progressive disease on alectinib monotherapy. If the CNS is a site of progressive disease on alectinib monotherapy, treatment of CNS lesions is required for enrollment. * The use of seizure prophylaxis is allowed as long as patients are taking non-enzyme inducing anti-epileptic drugs (non-EIAED). If patients were previously on EIAEDs and these have been discontinued, they must have been discontinued for at least 2 weeks prior to treatment start. If patients require an anti-epileptic medication, then a CYP3A4 non-EIAED can be used such as levetiracetam, valproic acid, gabapentin, topiramate or lacosamide. * Patients requiring steroids must be at a stable or decreasing dose for at least 1 week prior to enrollment * Patients with asymptomatic leptomeningeal disease are eligible for participation in this trial. However, patients who had progression of leptomeningeal disease on alectinib will be required to undergo CNS radiation to meet eligibility. Exclusion Criteria: * Participants who have had chemotherapy within 3 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier. * Participants who experienced progression of CNS lesions on alectinib who have not received local CNS therapies (radiation, surgery) to address the lesions. CNS imaging obtained at least 21 days after completion of radiation is required for confirmation of response. * Radiation therapy (except palliative to relieve bone pain) within 7 days of study entry. Palliative radiation (≤ 10 fractions) must have been completed at least 48 hours prior to study entry. Stereotactic or small field brain irradiation must have been completed at least 7 days prior to study entry. Whole brain radiation and radiation for leptomeningeal metastasis must have been completed at least 2 weeks prior to study entry. Acute effects of radiation must have resolved to baseline severity or to CTCAE grade ≤1 except for AEs that in the investigator's judgment do not constitute a safety risk for the patient. * Participants with uncontrolled tumor-related pain. * Symptomatic lesions amenable to palliative radiotherapy (e.g., bone metastases or metastases causing nerve impingement) should be treated prior to enrollment. * Asymptomatic metastatic lesions whose further growth would likely cause functional deficits or intractable pain (e.g., epidural metastases that are not currently associated with spinal cord compression) should be considered for loco-regional therapy if appropriate prior to enrollment. * Patients who are receiving denosumab prior to enrollment who are not willing and/or eligible to switch to a bisphosphonate while on study. * Pregnant or lactating women. * History of hypersensitivity to alectinib or any of its excipients. In addition, subjects who are unable to tolerate the 600 mg twice daily (BID) dose of alectinib will not be permitted to enroll unless doses of alectinib below the entry level are being investigated (e.g. dose level -1 and -2) and they have previously tolerated alectinib monotherapy at the dose being investigated. * Participants with prior allogeneic stem cell or solid organ transplantation. * History of extensive, disseminated, bilateral or presence of Grade 3 or 4 interstitial fibrosis or interstitial lung disease including pneumonitis, hypersensitivity pneumonitis, interstitial pneumonia, interstitial lung disease, obliterative bronchiolitis or pulmonary fibrosis. Patients with history of prior radiation pneumonitis are not excluded. * Serum albumin \< 2.5 g/dL * Positive test for human immunodeficiency virus (HIV) or history of active tuberculosis * Current use or anticipated need for food or drugs that are known strong or moderate CYP3A4 inhibitors, including their administration within 2 weeks prior to the first study treatment (ie, strong CYP3A4 inhibitors: grapefruit juice or grapefruit/grapefruit related citrus fruits \[eg, Seville oranges, pomelos\], ketoconazole, miconazole, itraconazole, voriconazole, posaconazole, clarithromycin, telithromycin, indinavir, saquinavir, ritonavir, nelfinavir, amprenavir, fosamprenavir nefazodone, lopinavir, troleandomycin, mibefradil, and conivaptan; Moderate CYP3A4 inhibitors: erythromycin, verapamil, atazanavir, delavirdine, fluconazole, darunavir, diltiazem, aprepitant, imatinib, tofisopam, ciprofloxacin, cimetidine). For participants in the dose escalation portion, no CYP3A4 inhibitors should be administered during the first 21 days of the study, regardless of strength. * Current use or anticipated need for drugs that are known strong or moderate CYP3A4 inducers including their administration within 2 weeks prior to the first study treatment (ie, phenobarbital, rifampin, phenytoin, carbamazepine, rifabutin, rifapentin, clevidipine, St. John's Wort). For participants in the dose escalation portion, no CYP3A4 inducers should be administered during the first 21 days of the study, regardless of strength. * Current symptomatic congestive heart failure or history of symptomatic congestive heart failure in the preceding 3 months, defined as New York Heart Association Classification 2- 4 * Left ventricular ejection fraction \< 50% or institutional lower limit of normal, whichever is lower * Current diagnosis of symptomatic bradycardia * Abnormal hematologic and end organ function, defined by the following laboratory results: * Absolute neutrophil count \< 1500 cells/uL (granulocyte colony-stimulating factor support should not be used within 2 weeks prior to Cycle 1, Day 1). * Platelet count \< 100,000/uL * Hemoglobin \< 9.0 g/dL (patients may be transfused above this threshold) * INR and aPTT \> 1.5 x ULN (upper limit of normal) * This applies only to patients who are not receiving therapeutic anticoagulation. Patients receiving therapeutic anticoagulation should be on a stable dose. * Serum creatinine \> 1.5x the ULN or an estimated glomerular filtration rate (eGFR) calculated using the Modification of Diet in Renal Disease (MDRD) equation of \< 45 mL/min/1.73 m2 * Serum lipase \> 1.5x ULN * Liver disease characterized by: * Alanine aminotransferase and asparate aminotransferase (ALT or AST) \> 3x ULN (or \> 5x ULN for patients with concurrent liver metastasis) confirmed on two consecutive measurements OR * Serum bilirubin \> 1.5 x ULN. Patients with known Gilbert's disease who have a serum bilirubin level \> 3 x ULN may be enrolled. * Impaired synthetic function or other conditions of decompensated liver disease, such as coagulopathy, hepatic encephalopathy, ascites, and bleeding from esophageal varices * Acute viral or active autoimmune, alcoholic, or other types of acute hepatitis * History of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment, central serous chorioretinopathy, retinal vein occlusion (RVO), or neovascular macular degeneration. Patients will be excluded from study participation if they are currently known to have any of the following risk factors for RVO: * Glaucoma with intraocular pressure ≥ 21 mmHg * Grade ≥ 2 serum cholesterol (patients with a history of elevated cholesterol controlled with lipid lowering medication to Grade ≤ 1 are eligible) * Grade ≥ 2 hypertriglyceridemia (patients with a history of elevated cholesterol controlled with lipid lowering medication to Grade ≤ 1 are eligible) * Grade ≥ 2 or symptomatic hyperglycemia (fasting). Hyperglycemia may be corrected with medications to Grade ≤ 1. * Grade ≥ 2 uncontrolled hypertension (patients with a history of hypertension controlled with anti-hypertensive medication to Grade ≤ 1 are eligible) * Major surgical procedure other than for diagnosis within 28 days prior to Cycle 1, Day 1 or anticipation of need for a major surgical procedure during the course of the study. * Evidence of active malignancy (other than current NSCLC, non-melanoma skin cancer, in situ cervical cancer, papillary thyroid cancer, localized/stable renal masses, ductal carcinoma in-situ/lobular carcinoma in-situ (DCIS/LCIS) of the breast, or localized and presumed cured prostate cancer) within the last 3 years. * Active inflammatory gastrointestinal disease or previous gastric resection or lap band. * Inability or unwillingness to swallow pills * Concurrent use of other tyrosine kinase inhibitors * Prior treatment with a mitogen activated kinase pathway (MAPK) inhibitor * Allergy or hypersensitivity to components of the cobimetinib formulation * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that would preclude the use of an investigational drug or that may affect the interpretation of the results or render the participant at high risk from treatment complications.