Has inadequate venous access and/or contraindications to leukapheresis Major surgery within 28 days of study day 1 with the exception of biopsy and insertion of central venous catheter. Subject is fit for leukapheresis and has adequate venous access for the cell collection. Must have, or be willing to have an acceptable central catheter. (Port a cath, peripherally inserted central catheter [PICC-line], or central venous catheter) (Insertion only required if randomized to Arm A). Major surgery within 28 days of day 1 (does not include central venous access or shunts) Poor peripheral venous access Inability to undergo venipuncture and/or tolerate venous access Adequate central venous access potential Central venous access, such as a Portacath or Hickman Line DONOR: Inability to achieve adequate venous access Major surgery within 28 days prior to the start of BGB324 - excluding skin biopsies and procedures for insertion of central venous access devices Major surgery, excluding skin biopsies and procedures for insertion of central venous access devices, within 28 days prior to the start of COTI-2. Adequate venous access (for leukapheresis and blood draws) DONOR: must have adequate peripheral venous access for leukapheresis or must agree to placement of a temporary central venous catheter Patients with inadequate bilateral peripheral venous or central venous catheter access for the required apheresis to allow generation of the autologous AdHER2 DC vaccine product Must have, or be willing to have an acceptable central catheter. (Port a cath, peripherally inserted central catheter [PICC] line, or central venous catheter) At least 7 days after minor surgery (such as central venous access) or biopsy and recovery to =< grade 1 treatment-related toxicity Research participant must have appropriate venous access Presence of any indwelling line or drain (e.g., percutaneous nephrostomy tube, indwelling Foley catheter, biliary drain, or pleural/peritoneal/pericardial catheter). Ommaya reservoirs and dedicated central venous access catheters such as a Port-a-Cath or Hickman catheter are permitted Poor venous access for study drug administration Adequate venous access for apheresis as assessed by apheresis team; NOTE: If a central venous catheter is required for apheresis, the patient is not eligible Subject has sufficient venous access to permit administration of study drug (for the IV cohorts), collection of pharmacokinetic samples and monitoring of safety laboratories. Major surgery (excluding skin biopsies and procedures for insertion of central venous access devices) within 2 weeks of first dose of study drug Presence of any indwelling line or drain. Dedicated central venous access catheter such as a Port-a-Cath or Hickman catheter are permitted. Must have adequate venous access for apheresis; (pheresis catheter placement for cell collection is allowed) Inability to be venipunctured and/or tolerate venous access Major surgery within 28 days prior to the start of BGB324, excluding skin biopsies and procedures for insertion of central venous access devices Have inadequate venous access for or contraindications to leukapheresis Must have adequate venous access for apheresis Subjects must not have inadequate venous access for or contraindications to leukapheresis Research participant must have appropriate venous access Research participant must have appropriate venous access If research participant is undergoing leukapheresis he/she must have appropriate venous access Central vascular access device(s) (e.g. infusaport, tunneled central veinous catheter [CVC] &/or peripherally inserted central catheter [PICC] line) providing a combined 3 access ports is advised for all patients Have access via central line (e.g., portacath) RECIPIENT: Adequate central venous access potential MATCHED RELATED DONOR: Adequate venous access for peripheral apheresis, or consent to use a temporary central venous catheter for apheresis DONOR: Donor must have adequate peripheral venous catheter access for leukapheresis or must agree to placement of a central catheter Adequate central venous access potential MATCHED RELATED DONOR: Adequate venous access for peripheral apheresis, or consent to use a temporary central venous catheter for apheresis, if applicable HAPLOIDENTICAL RELATED DONOR: Adequate venous access for peripheral apheresis, or consent to use a temporary central venous catheter for apheresis (if applicable) DONOR: Adequate venous access for peripheral leukapheresis, or consent to use a temporary central venous catheter for leukapheresis DONOR: Willing to have a central venous catheter placed for apheresis if peripheral veins are inadequate Venous access: a double lumen central vascular access device or its equivalent and an additional peripherally inserted central catheter (PICC) line will be required for all patients entered on protocol Willingness to have a central venous line (peripherally inserted central catheter [PICC] or PORT) Adequate intravenous (IV) access Poor or unsuitable venous access Poor venous access for study drug administration unless patient can use silicone based catheters (Prior to treatment) Note: evaluate at least 1 week before T cell infusion. a. Adequate venous access – consider peripherally inserted central catheter (PICC) or central line. b. ECOG/Zubrod performance status of ‘0-1. c. Bi-dimensionally measurable disease by palpation on clinical exam, or radiographic imaging (X-ray, computed tomography [CT scan]). d. At least 4 weeks must have elapsed since the last chemotherapy, immunotherapy, radiotherapy or major surgery. At least 6 weeks for nitrosoureas, mitomycin C and liposomal doxorubicin. e. Toxicity related to prior therapy must either have returned to =< grade 1, baseline, or been deemed irreversible. f. Persons of reproductive potential must agree to use and utilize an adequate method of contraception throughout treatment and for at least 3 months after study drug is stopped. g. Willing and able to give informed consent. Adequate vein access: consider peripherally inserted central catheter (PICC) or other central line Poor peripheral venous access Patient has or is willing to have a central venous catheter (e.g. PICC, Port-A-Cath®, Hickman® catheter) for drug administration. Inability to tolerate venous access Reliable venous access suitable for weekly study drug infusions Adequate central venous access potential Lack of peripheral venous or central venous access or any condition that would interfere with drug administration or collection of study samples Subject is fit for leukapheresis and has adequate venous access for the cell collection. Inability to be venipunctured and/or tolerate venous access Have a central venous catheter line in place prior to study treatment administration Have insufficient peripheral venous access to permit completion of the study dosing and compliance with study phlebotomy regimen Adequate venous access - consider peripherally inserted central catheter (PICC) or central line Adequate IV access Suitable venous access Inability to obtain venous access in the antecubital region to administer PHO or sedation for endoscopy procedures Participants who will have a central access catheter or a peripheral intravascular central catheter (PICC) should schedule this procedure at least 10 days prior to the start date of study drug HAPLO-IDENTICAL DONOR: The donor must have adequate peripheral venous catheter access for leukapheresis or must agree to placement of a central catheter DONOR: Donor must have adequate peripheral venous catheter access for leukapheresis or must agree to placement of a central catheter Must have adequate venous access for apheresis. Adequate IV access A vascular access device (port) or other central venous access for administration of chemotherapy is recommended Central venous access, such as a Portacath or Hickman Line Absence of central venous access for administration of the study drug DONOR: Donor must consent to placement of a central venous catheter in the event that peripheral venous access is limited Patients must consent to an indwelling central venous catheter DONOR: Inability to achieve adequate venous access DONOR: Must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral or subclavian) DONOR: Inability to achieve adequate venous access Adequate venous access Adequate venous access Must have a pre-existing central venous access such as a port, Hickmann catheter or a peripherally inserted central catheter (PICC line) or be willing and able to have one inserted. Central venous access Does the subject have adequate venous access? Central venous access Adequate venous access Suitable venous access Adequate venous access Pre-existing functioning central venous catheter Patients must consent to an indwelling central venous catheter DONOR: Adequate venous access for peripheral apheresis, or consent to use a temporary central venous catheter for apheresis Subject is fit for apheresis and has adequate venous access for the cell collection. Functioning Central Venous Access Device Patients who only have a totally implanted port as their central venous access will not be eligible for this study Participant must have adequate venous or central access for irinotecan administration Has a preexisting functional central venous catheter available for study drug administration Inpatients who have central venous catheter (CVC) that has been in place for at least 14 days and is expected to remain in place at least for 30 days after enrollment Patients with multiple co-existing central venous catheters at the time of enrollment will not be enrolled; multiple lumens in a single catheter are acceptable Inadequate venous access per assessment of treating health care provider No known problems with peripheral IV or central line access Inadequate venous access (a single antecubital or equivalent venous access sites are required for study drug injection) Adequate peripheral venous access or available central venous catheter access for radiopharmaceutical administration Presence of any indwelling line or drain. Note: Dedicated central venous access catheters such as a Port-a-Cath are permitted. Subjects with a central venous line Inadequate venous access Inadequate venous access per assessment of treating health care provider Inadequate venous access (two antecubital or equivalent venous access sites) Suitable venous access for the study-required blood sampling and consent for the specific amounts that will be taken. Agree to serial blood and bone marrow sampling Suitable venous access for the study-required blood sampling. Suitable venous access for the study-required blood sampling, including pharmacokinetic (PK) sampling. Must be amenable to serial bone marrow aspirates and peripheral blood sampling during the study. Ability to swallow oral medications, willingness to perform mucositis prophylaxis, and suitable venous access for the study-required blood sampling. Provide informed consent for genetic sampling and analyses Patients must agree to research blood sampling to participate in study Suitable venous access for the study-required blood sampling, including pharmacokinteic (PK) and pharmacodynamic (PD) sampling and blood transfusion support. Patients must agree to blood sampling to participate in study Able to comply with the protocol, including tissue and blood sampling Have agreed to undergo serial blood and bone marrow sampling. Subjects must be amenable to serial bone marrow biopsies, peripheral blood sampling, and urine sampling during the study. Patient must be amenable to serial peripheral blood sampling, urine sampling, and tumor biopsies during the study Have consented to undergo mandatory serial peripheral whole blood and tumor tissue sampling. Suitable venous access for the study-required blood sampling. Suitable venous access for the study required blood sampling (that is, including pharmacokinetic (PK) and biomarker sampling). Patient must be willing to submit the blood sampling and bone marrow sampling for the PK and PD analyses and exploratory biomarkers Ability to swallow oral medications, willingness to perform mucositis prophylaxis, and suitable venous access for the study-required blood sampling. Suitable venous access for the study-required blood sampling. Subjects must be amenable to serial peripheral blood sampling, urine sampling, and biopsies during the study. Subjects must be amenable to serial bone marrow sampling, peripheral blood sampling and urine sampling during the study. Suitable venous access for the study-required blood sampling Patients must agree to research blood sampling to participate in study Patients must be available for periodic blood sampling, study-related assessments, and management of toxicity at the treating institution Has suitable venous access for the study-required blood sampling. Unwilling to consent to genomics sampling Subjects must be amenable to peripheral blood sampling, urine sampling, and biopsies during the study. Subjects with AITL must also be amenable to serial bone marrow biopsies Suitable venous access for the study-required blood sampling, including pharmacokinetics. Adequate venous access for repeated blood sampling according to study schedule; Suitable venous access for the study-required blood sampling for MLN4924 pharmacokinetic (PK) and pharmacodynamic assessments. Suitable venous access for the study-required blood sampling Suitable venous access for the study-required blood sampling Willing to submit the blood sampling and bone marrow sampling required by protocol Participants must be willing to submit the blood sampling and bone marrow sampling for the pharmacokinetic (PK) and pharmacodynamic analyses and exploratory biomarkers Lack of suitable venous access for the study-required blood sampling for TAK-659. Suitable venous access for the study-required blood sampling (including pharmacokinetic [PK] sampling). Suitable venous access for the study-required blood sampling that is, including PK and pharmacodynamic sampling. Suitable venous access for the study-required blood sampling (including PK sampling). Suitable venous access for the study-required blood sampling (that is, PK). Suitable venous access for the study-required blood sampling, including PK and pharmacodynamic (PD) sampling.