Study of Vemurafenib, Carboplatin, and Paclitaxel

Study Groups: If you are found to be eligible and decide to take part, you will be assigned to a study group based on when you join this study. Up to 8 groups of 3-6 participants will be enrolled in this study. The dose of vemurafenib and the doses of carboplatin and paclitaxel you receive will depend on when you joined this study. The first group of participants will receive the lowest dose level of vemurafenib, carboplatin, and paclitaxel. Each new group will receive a higher dose level of the study drug combination than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of the combination is found. After that, 10 additional participants will be enrolled. Study Drug Administration: Each study cycle is 3 weeks. You will start taking paclitaxel and carboplatin on Day 1 of Cycle 1. Paclitaxel will be given by vein over 3 hours, and carboplatin will be given by vein over 30-60 minutes. You may be given medications to reduce the risk of nausea and allergic reaction before these study drugs are given. Both paclitaxel and carboplatin will be given every 3 weeks. You will start taking vemurafenib by mouth in the evening on Day 1 of Cycle 1. You will then take vemurafenib twice a day, every day starting with Day 2 of Cycle 1. Study Visits: At every study visit, you will be asked about any drugs you may be taking, how you are feeling, and if you have had any side effects. On Day 1 of Cycle 1: * You will have a physical exam, including measurement of your weight and vital signs if not done in the past 8 days. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests if this was not done in the past 10 days. On Day 8 of Cycle 1: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. On Day 1 of Cycles 2 and beyond: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. * In Cycle 2 only, you will have an ECG. After Cycle 4, if you are tolerating the study drug combination well and the study doctor agrees, you may have your Day 1 visit every other cycle. Every 6 weeks (every 2 cycles), you will have a CT scan, MRI scan, bone scan, and/or x-ray to check the status of the disease. Length of Study Participation: You may continue taking the study drug combination for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drugs if the disease gets worse, if you start having other health problems, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over when you have completed the End-of-Study Visit. End-of-Study Visit: Within 4 weeks after your last dose of study drugs: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. * You will have an ECG. * You will have a CT scan, MRI scan, bone scan, and/or x-ray to check the status of the disease. This is an investigational study. Vemurafenib is FDA approved and commercially available to treat advanced melanoma with mutated BRAF. Carboplatin and paclitaxel are FDA approved for certain types of cancers, including lung and ovarian cancers. Using the study drug combination to treat advanced cancer with a BRAF mutation is considered investigational. Up to 96 participants will be enrolled in this study. All will take part at MD Anderson.