Vemurafenib in Combination With Everolimus or Temsirolimus With Advanced Cancer

Study Drug Administration: If you are found to be eligible to take part in this study, your doctor will decide whether you will receive either everolimus or temsirolimus You will be assigned to a dose level of vemurafenib based on when you join this study. Up to 5 dose levels of vemurafenib will be tested. Up to 6 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of vemurafenib is found. Study Drug Administration: You will take 3 vemurafenib tablets in the morning and 3 tablets in the evening.You will take it every day during each 28-day study cycle. You will take vemurafenib in combination with either 1 tablet of everolimus every day of each cycle or you will receive temsirolimus by vein over 30-60 minutes on Days 1, 8, 15, and 22 of each cycle. You will receive a dosing diary to record ONLY the date and times when you did NOT take a scheduled dose of the study drug. You should bring this diary and any used or unused study drug bottles to your next study visit (even empty bottles must be returned). Study Visits: At all study visits, you will be asked about any drugs you may be taking and if you have had any side effects from them. On Days 1 and 15 of Cycle 1 and Day 1 of Cycle 6: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have an ECG (Day 15 only) On Day 1 of Cycles 2 and 5: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have an ECG. * Your skin will be checked. * You will have a CT scan or MRI scan to check the status of the disease (Cycle 5 only). On Day 1 of Cycle 3: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have an ECG. * You will have a CT scan or MRI scan to check the status of the disease. On Day 1 of Cycle 4: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have an ECG. * You will have a head and neck exam to check the status of the disease. On Day 1 of Cycle 7: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have a CT scan or MRI scan to check the status of the disease. * You will have a head and neck exam to check the status of the disease. On Day 1 of Cycles 8 and beyond: * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. After Cycle 7, every 12 weeks: * You will have an ECG. * You will have a head and neck exam to check the status of the disease. * Your skin will be checked. On Day 1 of every 2 cycles: °You will have a CT scan or MRI scan to check the status of the disease. Length of Study: You may continue taking the study drugs 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 intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over once you have completed the follow-up. End of Study Drug Dosing Visit: Once you are no longer taking the study drug, you will have a study visit. At this visit: * You will be asked about any drugs you may be taking and if you have had any side effects from them. * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests. * You will have an ECG. * You will have a CT scan or MRI scan to check the status of the disease. * Your skin will be checked. Safety Follow-Up Visit: If you leave the study for any reason other than the disease getting worse, you will have a follow-up visit about 28 days after your last dose. At this visit: * You will be asked about any drugs you may be taking and if you have had any side effects from them. * You will have an ECG. * Your skin will be checked. * You will have a head and neck exam to check the status of the disease. Follow-Up: Every 3 months after the last dose of study drug (for up to 12 months) you will be contacted by phone and asked about any new drugs you may be taking. This should take less than 5 minutes. This follow up may be during a regularly scheduled clinic visit. Participant Responsibilities: * Take the study drug as instructed by the study staff. * Keep your study appointments. If you cannot keep an appointment, reschedule as soon as you know that you will miss the appointment. * Tell your doctor or study staff about any side effects, doctor visits, or hospitalizations that you may have. * Keep the study drug in a safe place, for your use only, and away from children. It must be stored at room temperature but not warmer than 77 degrees F (25 degrees Celsius). * Complete your diaries as instructed * While on this study, you cannot take part in any other research project without approval from your doctor. This is an investigational study. Vemurafenib is FDA-approved for metastatic melanoma. Its use in other types of cancer is investigational. Everolimus and temsirolimus are FDA approved kidney cancer. The combination of these drugs is investigational. Up to 114 participants will be enrolled in this study. All will take part at MD Anderson.