Patients requiring daily systemic corticosteroids are not eligible; patients must not have received systemic corticosteroids within 7 days prior to enrollment; if used to modify immune adverse events related to prior therapy, >= 14 days must have elapsed since last dose of corticosteroid; Note: use of topical or inhaled corticosteroids will not render a patient ineligible Has received more than 2 days of systemic corticosteroids for aGVHD. Patients on any systemic corticosteroid therapy within one week before the planned date for first dose on study would not be eligible; exception: patients on physiologic replacement doses of corticosteroids are permitted Any condition that would prohibit administration of corticosteroids Conditions that would prohibit administration of corticosteroids Patients must not have received any immunosuppressive medication within 28 days prior to sub-study registration and must not be planning to receive these medications while on protocol therapy; systemic corticosteroids must be stopped at least 24 hours prior to sub-study registration; however, intranasal and inhaled corticosteroids are allowed at any time before and during protocol therapy NO patients receiving systemic corticosteroids (either intravenous [IV] or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Patients receiving chronic pharmacologic doses of corticosteroids are not eligible; for the purposes of eligibility, chronic exposure is defined as anticipated exposure of > 3 weeks, including the sum of both pre-enrollment and anticipated post-enrollment dosing; patients on acute corticosteroid therapy (=< 3 weeks of total planned exposure) must still meet the normal blood glucose requirement; patients receiving chronic inhaled corticosteroids or chronic physiologic replacement doses of corticosteroids are eligible It is preferred, but not required, that corticosteroids and hydroxyurea should start only after all diagnostic samples have been obtained; however, if the patient was previously on corticosteroids and/or hydroxyurea, this is allowable provided that the patient still has measurable disease at time of the bone marrow aspirate\r\n* Corticosteroids and/or hydroxyurea, as well as any of the other therapies mentioned (with the exception of IV cyclophosphamide), may continue to be administered, at physician discretion, until 1 day prior to blinatumomab administration\r\n** IV cyclophosphamide must be discontinued at least 7 days prior to blinatumomab administration Treatment with systemic immune modulators including, but not limited to, non-topical systemic corticosteroids, cyclosporine, and tacrolimus within 2 weeks before enrollment (day 1). Patients receiving systemic corticosteroids (patients off steroids for at least 48 hours are eligible) Patients must not be receiving chronic systemic corticosteroids at doses greater than physiologic dosing (inhaled corticosteroids acceptable). Are receiving increasing doses of corticosteroids Patients must have no clinical evidence of leptomeningeal or brain metastasis causing spinal cord compression that are symptomatic or untreated or not stable for >= 3 months (must be documented by imaging) or requiring corticosteroids; subjects on a stable dose of corticosteroids > 1 month or who have been off of corticosteroids for at least 2 weeks can be enrolled with approval of the Cancer Therapy Evaluation Program (CTEP) medical monitor; subjects must also be off of enzyme-inducing anticonvulsants for > 4 weeks Use of corticosteroids (glucocorticoids) within 21 days of the MILs collection TREATMENT: Patients receiving systemic corticosteroids Patients must have previously untreated disease (except for one week or less of corticosteroids) Received corticosteroids within the past 1 week Patients receiving systemic corticosteroids (patients off steroids for at least 48 hours are eligible) Patients receiving corticosteroids are eligible for this trial Participants who have received 2 or more systemic treatment for cGvHD in addition to corticosteroids ± CNI for cGvHD Patients that transition from active aGvHD to cGvHD without tapering off corticosteroids ± CNI and any systemic treatment * Patients receiving up to 30 mg by mouth once a day of hydrocortisone (i.e., physiologic replacement dose) of corticosteroids are allowed. Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of the study drugs. No history of long-term use of corticosteroids or concurrent short term use of corticosteroids is allowed Subjects, who have received previous systemic corticosteroids treatment or poorly absorbable corticosteroids for the treatment of aGVHD, for longer than 3 days (72 hours). Subject who used corticosteroids (excluding inhalers, eye-drops, and dermatologic corticosteroids) within 6 weeks prior to surgery; Patients may not be on immunosuppressive therapy, including corticosteroids (with the exception of physiologic replacement, defined as 0.75 mg/m^2/day) at time of enrollment; however, patients who require intermittent use of bronchodilators or local steroid injections will not be excluded from the study Patient is receiving unstable or increasing doses of corticosteroids. Systemic corticosteroids are permissible in the following circumstances:\r\n* Short course systemic corticosteroids for disease control, improvement of performance status or non-cancer indication (=< 7 days) must have been discontinued at least 7 days prior to study treatment\r\n* Ongoing administration of a stable dose of corticosteroid therapy (previously received for >= 30 days) is permissible provided there is evidence of measurable disease and there will be no increase in steroid dose during the clinical trial Patients receiving systemic corticosteroids (patients off steroids for at least 48 hours are eligible) Chronic use of immune-suppressive drugs (ie, systemic corticosteroids used in the management of cancer or non-cancer related illnesses, eg, COPD). No systemic corticosteroids (unless physiologic replacement dosing) within 7 days of enrollment Patients who have received high doses of systemic corticosteroids for the treatment of their ATL within 4 weeks prior to the start of therapy Concurrent systemic treatment or prior therapy within 4 weeks for SMM; NOTE: Treatment with corticosteroids for other indications is permitted Use of corticosteroids or other immunosuppression (if patient had been taking steroids, at least 2 weeks must have passed since the last dose) Patients receiving systemic corticosteroids greater than 2-weeks in duration within 6 months of study entry must have evidence of adequate adrenal function based upon morning plasma cortisol concentration or ACTH (cosyntropin) stimulation test Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug. Need for systemic treatment with corticosteroids for cGVHD Received any previous systemic treatment for cGVHD with the exception of corticosteroids administered for cGVHD within the 72 hours prior to signing the informed consent form. Corticosteroids Concurrent systemic corticosteroids, cytokines, and immunomodulatory therapy (e.g. interferons) Patients receiving concurrent corticosteroids at the time protocol therapy is initiated other than for physiologic maintenance treatment No systemic corticosteroids (unless physiologic replacement dosing) within 7 days of enrollment Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids No systemic corticosteroids (unless physiologic replacement dosing) within 7 days of enrollment Patients who are receiving systemic corticosteroids Off all but replacement dose of corticosteroids from Day -7 to Day 28 (replacement dose is the patient's individualized dose defined for physiological replacement). Use of systemic corticosteroids Off all but replacement dose of corticosteroids from Day -7 to Day 28 (replacement dose is the patient's individualized dose defined for physiological replacement). Chronically treated with systemic doses of immunosuppressive drugs such as cyclosporin, ACTH, or corticosteroids. Any condition that requires the use of corticosteroids outside of corticosteroids defined in the protocol after day 1 of therapy Patients who are on corticosteroids or immunosuppressant’s are not eligible; a 2 week wash-out period for is required before registration Patients who have received systemic corticosteroids within 28 days prior to the first dose of study drug 1% prednisolone acetate ophthalmic suspension and any other corticosteroids. Patients receiving corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Patients receiving systemic corticosteroids (either intravenous [IV] or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Subjects requiring daily corticosteroids either via oral route of administration (po) or infusion. Patient has history of primary immunodeficiency OR has received any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment, excluding intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses; attempts should be made to have patient on lowest possible dose of steroids (acceptable range 4-10 mg, please contact PI if dose is > 4 mg) and weaned to off as is feasible Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Any concurrent treatment that would compromise the study including but not limited to continuous high dose corticosteroids (>0.5mg/kg), lymphodepleting antibodies or cytotoxic agents. Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Subject requires or is likely to require more than a two-week course of corticosteroids for intercurrent illness; subject must complete the course of corticosteroids 2 weeks before screening to meet eligibility Patients being chronically treated with immunosuppressive drugs such as cyclosporin, adrenocorticotropic hormone (ACTH), or systemic corticosteroids Conditions that would prohibit administration of corticosteroids No systemic corticosteroids (unless physiologic replacement dosing) within 7 days of enrollment Any condition that requires or is likely to require treatment with systemic corticosteroids within the core study period and short term follow-up Subjects who require or are likely to require more than a two-week course of corticosteroids for intercurrent illness; subjects must complete therapy prior to enrollment; topical corticosteroids should be stopped at least 2 weeks prior to enrollment and systemic corticosteroids should be stopped at least 4 weeks prior to enrollment Conditions that would prohibit intermittent administration of corticosteroids for T-DM1 premedication. Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids, such as systemic cyclosporine and tacrilomus; consult principal investigator for questions, including necessary washout period for the specific drug Patients must have no clinical evidence of leptomeningeal or brain metastasis causing spinal cord compression that are symptomatic or untreated or not stable for >= 4 weeks (must be documented by imaging) or requiring corticosteroids; subjects on a stable dose of corticosteroids > 1 month or who have been off of corticosteroids for at least 2 weeks can be enrolled with approval of the Cancer Therapy Evaluation Program (CTEP) medical monitor; subjects must also be off of enzyme-inducing anticonvulsants for > 4 weeks Treatment with corticosteroids within 4 weeks prior to enrollment Patients taking systemic corticosteroids Fixed or decreasing dose of corticosteroids (or no corticosteroids) for at least 1 week prior to cycle 1 day 1 The use of corticosteroids to control cerebral edema or treat neurologic symptoms will not be allowed, and patients who previously required corticosteroids for symptom control must be off steroids for at least 3 days without recurrence of symptoms prior to starting trial therapy; corticosteroids for other indications is allowed Current use of systemic corticosteroids More than 4 weeks since prior systemic corticosteroids Corticosteroids by aerosol are allowed Patients who have received systemic chemotherapy (corticosteroids not included) less than 3 weeks prior to the start of this protocol Any therapy =< 2 weeks prior to registration; NOTE: Exception: patients on ibrutinib or corticosteroids (any dose) may continue therapy up until the new regimen has started at investigator discretion; corticosteroids can be tapered to lowest possible dose after start of treatment at investigator discretion Patients receiving unstable or increasing doses of corticosteroids Patients must have discontinued systemic antineoplastic therapy (including endocrine and biological agents, as well as systemic corticosteroids) at least three (3) to four (4) weeks prior to enrollment. Toxicities from previous therapies must be grade 1 or less. Neurological symptoms related to underlying disease requiring increasing doses of corticosteroids Patient received corticosteroids within 2 weeks prior to the first dose. At least 2 weeks beyond corticosteroids. Patients who have received corticosteroids =< 2 weeks prior to starting study drug; the exception is patients receiving low dose steroids for CNS disease; otherwise, systemic corticosteroids should not be administered with BKM120 Immunosuppression (corticosteroids to prevent brain edema are permitted) ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Daily administration of systemic immunosuppressive therapy or corticosteroids (except in physiological doses for hormone deficiency) during the previous 30 days Any use of systemic corticosteroids within 10 days of treatment initiation. Patients must not be receiving chronic systemic corticosteroids at doses greater than physiologic dosing (inhaled corticosteroids acceptable). Patients requiring systemic corticosteroids (unless patients have had no corticosteroids within 4 weeks prior to start of study) Subjects require or are likely to require more than a 2-week course of corticosteroids for intercurrent illness. Subjects must have completed the course of corticosteroids at the time of apheresis to meet eligibility. No prior therapy is allowed except for the following:\r\n* Short courses of corticosteroid (defined as =< 7 days of corticosteroids within the 4-weeks preceding registration) are allowed\r\n** Participants who have been on corticosteroids chronically (defined as more than 7 days of corticosteroids within the 4-weeks preceding registration or more than 28 days of corticosteroids over the preceding 6 months) are not eligible; previous courses of inhaled corticosteroids of any duration are allowed\r\n* A single dose of intrathecal cytarabine (at the time of the diagnostic lumbar puncture) is allowed prior to registration; if patient has received intrathecal (IT) cytarabine prior to informed consent for protocol treatment, day 1 IT cytarabine should not be administered\r\n* Emergent radiation to the mediastinum or other life-threatening masses is allowed prior to registration The subject requires or is likely to require more than a 2-week course of corticosteroids of > 4 mg Treatment with systemic corticosteroids within 2 weeks prior to the start of the treatment; patients that require inhaled or low-dose corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, mineralocorticoids are allowed Patients who are currently receiving or plan to receive corticosteroids except as described below \r\n* Systemic corticosteroids may be administered for cytoreduction up to 24 hours prior to the start of protocol therapy, as a premedication for InO and as treatment for allergic reactions or for physiologic replacement/stress dosing of hydrocortisone for documented adrenal insufficiency; corticosteroids are not allowed for other indications No oral corticosteroids 3 days before initiating combinations TEW-7197/POM; inhaled corticosteroids are permitted Has had systemic corticosteroids within 2 weeks of the first dose of protocol-related radiation or MK-3475 Leptomeningeal or brain metastases or metastases causing spinal cord compression that are symptomatic or untreated or not stable for >= 3 months (must be documented by imaging) or requiring corticosteroids; subjects on a stable dose of corticosteroids > 1 month or who have been off of corticosteroids for at least 2 weeks can be enrolled with approval of the Cancer Therapy Evaluation Program (CTEP) medical monitor; subjects must also be off of enzyme-inducing anticonvulsants for > 4 weeks No prior therapy is allowed except for the following:\r\n* Corticosteroids: short courses of corticosteroid (defined as =< 7 days of corticosteroids within the 4 weeks preceding registration) are allowed prior to registration; note: if patient has received pre-treatment with corticosteroids, they should not receive steroid prophase\r\n** Participants who have been on corticosteroids chronically (defined as more than 7 days of corticosteroids within the 4 weeks preceding registration or more than 28 days of corticosteroids over the preceding 6 months) are not eligible\r\n* IT cytarabine: a single dose of intrathecal cytarabine (at the time of the diagnostic lumbar puncture) is allowed prior to registration; if patient has received IT cytarabine prior to registration, day 1 IT cytarabine should not be administered\r\n* Emergent radiation therapy: emergent radiation to the mediastinum or other life-threatening masses is allowed prior to registration Participants who have received more than 7 days of corticosteroids in the preceding 4 weeks or more than 28 days of corticosteroids in the preceding 6 months are not eligible Corticosteroids should not be used during chemotherapy administration as an antiemetic Any condition that would prohibit administration of corticosteroids Patient must have received no prior radiation therapy or chemotherapy other than corticosteroids; corticosteroids are allowable for all patients Any use of systemic corticosteroids in the prior 4 weeks Patients requiring treatment with corticosteroids are eligible Patients receiving chronically dosed corticosteroids within 7 days prior to enrollment are not eligible for this trial Conditions that would prohibit administration of corticosteroids Patients taking systemic corticosteroids Subjects who cannot tolerate a corticosteroid taper, that is, begin corticosteroids at 2.0 mg/kg per day, demonstrate response, but progress before a 50% decrease from the initial starting dose of corticosteroids is achieved. Concurrent, recent (? 4 weeks ago) or anticipated treatment with systemic corticosteroids at any dose, or Requiring corticosteroids or anticonvulsants in the prior 60 days Concurrent, recent (? 4 weeks ago) or anticipated treatment with systemic corticosteroids at any dose, or Requiring corticosteroids or anticonvulsants in the prior 60 days Have had any chemotherapy or systemic corticosteroids within 2 weeks of study entry. Concurrent, recent (? 4 weeks ago) or anticipated treatment with systemic corticosteroids at any dose, or Daily administration of systemic immunosuppressive therapy or corticosteroids (except in physiological doses for hormone deficiency) during the previous 30 days. Systemic (oral or parenteral) corticosteroids within 14 days of study entry Current use of systemic corticosteroids Patients receiving corticosteroids are not eligible; patients must have been off corticosteroids for 7 days prior to start of chemotherapy Concurrent or planned concurrent treatment with systemic high dose (immunosuppressive) corticosteroids or treatment with systemic corticosteroids within 4 weeks of baseline Patients who have received oral or parenteral corticosteroids within 2 weeks of study entry or who have a clinical requirement for ongoing systemic immunosuppressive therapy not related to chemotherapy administration. Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids Systemic corticosteroids use =< 2 weeks, regardless of indication; note: patients who are on inhaled corticosteroids are eligible Patients receiving concurrent corticosteroids for reason(s) other than for physiologic maintenance treatment; patients should otherwise discontinue corticosteroids prior to registration to study Concurrent maintenance corticosteroids; No previous use of corticosteroids for autoimmune complications that have developed since the initial diagnosis of CLL; prior use of corticosteroids for reasons other than treatment of autoimmune complications is allowed History of long-term use of corticosteroids or concurrent short-term use of corticosteroids is not allowed; short-term corticosteroid use must be discontinued at least 2 weeks prior to study treatment Brain metastases that are symptomatic or untreated or not stable for >= 3 months (must be documented by imaging) or requiring corticosteroids; subjects on a stable dose of corticosteroids > 1 month or who have been off corticosteroids for at least 2 weeks can be enrolled with approval of the Cancer Therapy Evaluation Program (CTEP) medical monitor; subjects must also be off enzyme-inducing anticonvulsants for > 4 weeks Treatment with corticosteroids within 2 weeks Clinically stable and off corticosteroids for at least 4 weeks prior to study enrollment Patients receiving immunosuppressive treatment as well as corticosteroids which cannot be discontinued at least 4 weeks before dosing. Chronic use of corticosteroids Currently being treated with bronchodilators or corticosteroids Past or current anti-cancer treatment except corticosteroids during less than one week. Long-term use of systemic corticosteroids Patients receiving oral corticosteroids within 30 days of enrollment. For Dose Confirmation (Parts B, D, E, F and G): Have CNS metastasis that is radiographically or clinically unstable less than 14 days prior to receiving study drug, regardless of whether they are receiving corticosteroids For Dose Confirmation (Part C): Have glioblastoma multiforme that is radiographically or clinically unstable less than 14 days prior to receiving study drug, regardless of whether they are receiving corticosteroids Patients who have been treated for at least two weeks with stable doses of corticosteroids to address conditions unrelated to their malignancy will be allowed to continue this treatment during enrollment on the current trial Concurrent treatment with corticosteroids. If they are already on steroids, patients will be allowed to enroll on the study but will need to taper off as soon as possible. Subject requires or is likely to require more than a two week course of corticosteroids for intercurrent illness; subject must complete the course of corticosteroids 2 weeks before screening to meet eligibility Supraphysiologic doses of corticosteroids within 3 weeks Patients who have received systemic chemotherapy (corticosteroids not included) less than 3 weeks prior to the start of this protocol Subjects with a medical condition requiring chronic systemic corticosteroids Any other disease requiring long-term corticosteroids or immunosuppressants Patients must not be receiving chronic systemic corticosteroids at doses greater than physiologic dosing (inhaled corticosteroids acceptable). Subjects must be receiving systemic corticosteroids. Participants must be receiving systemic corticosteroids. Treatment with methylprednisolone/systemic steroids must have been initiated within 72 hours prior to the first dose of study treatment after enrollment Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids, such as systemic cyclosporine and tacrolimus No ongoing requirement for corticosteroids Daily requirement for corticosteroids (except for inhalation corticosteroids). Is receiving chronic corticosteroids administered at doses greater than those used for normal replacement therapy Is taking systemic corticosteroids (more than 3 consecutive days) or other immunomodulators or immune suppressive medication Patient has discontinued all corticosteroids for that indication for at least 2 weeks; Patients who require treatment with systemic corticosteroids for serious medical conditions or illnesses (e.g. immunosuppression after organ transplantation) Patients currently receiving systemic corticosteroids Patients on systemic corticosteroids (except for patients on stable doses of hormone replacement therapy such as hydrocortisone), or other immunosuppressants (e.g., infliximab, mycophenolate mofetil) are excluded For patients on corticosteroids, they must have been on a fixed dose for 1 week prior to entry if clinically recommended Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids Patients on corticosteroids for any reason Patients who have received systemic corticosteroids =< 2 weeks prior to starting study drug; systemic corticosteroids should not be administered with BKM120 (usage of steroids as premedications and anti-emetics for paclitaxel and carboplatin, per MSKCC guidelines, is allowed; steroids given as part of pre-medications for imaging studies are not exclusionary) Patients taking systemic corticosteroids patients receiving hydroxyurea or corticosteroids that has not been discontinued at least 1 week after initiation of nilotinib Prior corticosteroids allowed Patients must not require use of systemic corticosteroid within 14 days prior to registration or during protocol treatment; patients with preexisting severe autoimmune disease requiring systemic corticosteroids or ongoing immunosuppression are not eligible Patients must not be receiving any of the following concomitant medications:\r\n* Pharmacologic doses of systemic corticosteroids unless for CNS metastatic or primary disease; for patients with CNS metastatic or primary tumors receiving corticosteroids, they should be on a stable or decreasing dose over the 7 days prior to registration; for all patients, receipt of systemic physiologic replacement steroids, topical, and/or inhaled corticosteroids is acceptable\r\n* Non-steroidal anti-inflammatory drugs, oral anticoagulants, and therapeutic heparins Treatment with high dose systemic corticosteroids or continuous use of other immunosuppressants within the past 30 days Current use of corticosteroids defined as oral, intravenous (IV), or injections of corticosteroids in the past 4 weeks\r\n* If the patient is only prescribed a short-term, time-limited dose of oral, intravenous (IV), or injections of corticosteroids, then they may be rescreened for eligibility once they are >= 4 weeks post-completion of their course of corticosteroids Use of oral corticosteroids or topical corticosteroids in the irradiation area Short course systemic corticosteroids is permissible for disease control, improvement of performance status or non-cancer indication if =< 10 days and must be discontinued prior to study treatment Patients receiving systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug Patients must not have received oral corticosteroids, intramuscular corticosteroids, or intra-articular steroids for joint symptoms within 28 days prior to registration Treatment with high dose systemic corticosteroids or continuous use of other immunosuppressants within the past 6 months Patients on chronic corticosteroids Patients on systemic corticosteroids (oral or intravenous) Treatment within 3 months with immunomodulatory therapy (e.g., interferons, immunoglobulin therapy, interleukin 1 receptor antagonist or systemic corticosteroids); short-term systemic corticosteroids or topical or intra-articular steroids are acceptable, at the discretion of the Investigator Corticosteroids: no restrictions