Study of Brentuximab Vedotin Plus TAK228 for Relapsed/Refractory Classical Hodgkin Lymphoma, Anaplastic Large Cell Lymphoma and Other CD30+Peripheral T-Cell Lymphomas

Study Groups: If you are found to be eligible to take part in this study, you will be assigned to a dose level of TAK228 based on when you join this study. Up to 4 dose levels of TAK228 will be tested. About 3-6 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 TAK228 is found. Your dose of brentuximab vedotin will stay the same. However, if the doctor thinks it is needed for your safety, it may be lowered. Study Drug Administration: Each cycle is 21 days. You will receive brentuximab vedotin by vein over about 30 minutes on Day 1 of each cycle. You will take TAK228 by mouth either every day or on a 5 days on/2 days off schedule (a "5/2 schedule," where you take the study drug every day for 5 days in a row and then do not take any TAK228 for 2 days in a row). The study doctor will tell you how often to take the study drug. Each dose of TAK228 should be taken at about the same time each day on an empty stomach with 8 ounces (about 1 cup) of water. You should fast for 2 hours before and 1 hour after each dose. Length of Study: You may receive up to 16 cycles of study drugs. 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 in this study will be over after about 2 years of follow-up (described below). Study Visits: One (1) time every week while receiving the study drugs, blood (about 1-2 tablespoons) will be drawn for routine tests. Within 3 days before the start of Cycles 2 and beyond: * You will have a physical exam. * Blood (about 1-2 tablespoons) will be drawn for routine tests and to check your blood sugar levels. If you can become pregnant, part of this blood sample will be used for a pregnancy test. You should fast for about 8-10 hours before this draw. * Urine will be collected for routine tests. * You will have an EKG. At the end of Cycle 1: °Blood (about 1-2 tablespoons) will be drawn for biomarker testing. At the end of Cycle 3 and every 3 cycles after that (Cycles 6, 9, 12, and so on), you will have a CT or PET/CT scan. At-Home Glucose Monitoring: You are required to monitor your glucose (sugar) levels at home during the first 2 months you are taking the study drug. If the doctor thinks it is needed, you may be asked to continue monitoring your glucose (sugar) levels at home. The study staff will give you a glucose monitor (called a glucometer) and teach you how and when to use it. You will bring the glucometer with you to each study visit so the study staff can collect the results of the testing. The study team will tell you what an "abnormal" level is and when to contact the study doctor/study staff. You will need to return the glucometer to the study staff at the end of the study. End-of-Dosing Visit: Within 21 days after your last dose of study drugs: * You will have a physical exam. * Blood (about 1-2 tablespoons) will be drawn for routine tests and to check your blood sugar levels. If you can become pregnant, part of this sample will be used for a pregnancy test. You should fast for about 8-10 hours before this draw. * Urine will be collected for routine tests. * You will have an EKG. * You will have a PET/CT or CT scan. Follow-Up: Every 4 months for up to 2 years: * You will have a physical exam. * Blood (about 1-2 tablespoons) will be drawn for routine tests and to check your blood sugar levels. You should fast for about 8-10 hours before this blood draw. * You will have a CT scan. If you are found to be eligible to receive a transplant as part of your standard care, you may receive a transplant. You will sign a separate consent explaining that procedure and its risks in more detail. If you have a stem cell transplant, you will stop having follow-up visits as part of this study.