Treatment within days prior to enrollment/randomization with strong immune modulators including but not limited to systemic cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, methotrexate, azathioprine, rapamycin, thalidomide, and lenalidomide Treatment with systemic immune modulators including, but not limited to, non-topical systemic corticosteroids, cyclosporine, and tacrolimus within weeks before enrollment (day ). Subjects with prior organ transplant or being treated, or anticipated to be treated, with cyclosporine (because long-term administration of the combination of cyclosporine and sirolimus is associated with deterioration of renal function). Treatment with steroids or immunosuppressive therapy such as cyclosporine, tacrolimus, anti-thymocyte globulin (ATG) within months of registration Last dose with any of the following agents including but not limited to: etanercept, infliximab, tacrolimus, cyclosporine, mycophenolic acid, alefacept, or efalizumab < days prior to first dose of study drug the subject has been off systemic immunosuppressive medications (including but not limited to: cyclosporine, tacrolimus, mycophenolate mofetil, or corticosteroids) for at least month prior to the first dose of GSK. Topical steroids are permitted Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Regular use of immunosuppressant drugs such as steroids (> mg prednisone equivalents), azathioprine, tacrolimus, cyclosporine, etc; use is not permitted within weeks before recruitment Patients requiring chronic systemic immunosuppressive medication including pharmacologic dose of glucocorticoids or cyclosporine should be evaluated by the Medical Monitor for enrollment eligibility. Only for subjects enrolled in Arm - Neratinib and everolimus: subjects requiring therapy with immunosuppressive agents such as anti-tumor necrosis factor alpha (TNFa) agents (etanercept, adalimumab), azathioprine, methotrexate, cyclosporine, etc. for active autoimmune disorder. History of clinically severe (e.g., requires chronic immunosuppressive therapy, [e.g., cyclosporine A, tacrolimus]) autoimmune disease (e.g., ulcerative colitis, lupus), or history of organ transplant Not currently receiving immunosuppressive drugs such as corticosteroids (excluding topical treatment), tacrolimus or cyclosporine ELIGIBILITY CRITERIA- LYMPHODEPLETION/INFUSION OF tvs-CTL: Must not be currently receiving immunosuppressive drugs such as corticosteroids (excluding topical treatment), tacrolimus or cyclosporine Patients must be on single immune suppression therapy with either tacrolimus or cyclosporine at the time of CD+ memory T-cell infusion; prednisone at a physiologic dose of mg per day or less is allowed Patients who are receiving cyclosporine, tacrolimus, or other chronic immunosuppressive agents are NOT eligible for participation Patients concurrently taking the following drugs are excluded: mycophenolate, cyclosporine, prednisone > mg/day, or immunosuppressive agents Known severe or life-threatening allergy or intolerance to fludarabine, alemtuzumab, cyclosporine, or mycophenolate mofetil. Use of systemic immunosuppressive medications, including corticosteroids, tacrolimus, mycophenolate mofetil, sirolimus or cyclosporine A Under active treatment with immunosuppressive agents such as systemic corticosteroids or cyclosporine that cannot be discontinued before starting rRp infusions Subject is receiving concomitant immunosuppressive therapy, defined as:\r\n* Immunosuppressants, including: tacrolimus, sirolimus, everolimus, cyclosporine, azathioprine, mycophenolate mofetil, antithymocyte globulin, basiliximab, belatacept\r\n* Systemic corticosteroids (except for short team treatment of allergic reactions or for treatment of immune related adverse events [irAE]); steroids with no or minimal systemic effect (topical, inhalation) are allowed\r\n* Chemotherapy\r\n* Immunotherapy\r\n* Monoclonal antibodies Patients concurrently taking the following drugs are excluded: mycophenolate, cyclosporine, prednisone > mg/day, or immunosuppressive agents Patient requiring chronic treatment with BCRP inhibitors (cyclosporine, eltrombopag) Patient must not have received immune suppressants: corticosteroids (for other than allergic reactions and anaphylaxis), cyclosporine or tacrolimus within days of enrollment\r\n* Note: the use of topical and/or inhalational steroids is allowed Patients must not be currently receiving immunosuppressive drugs such as corticosteroids, tacrolimus or cyclosporine Patients on tacrolimus or any other immunosuppressants with significant interaction with cisplatin Other immunosuppressive medications such as methotrexate, cyclosporine, azathioprine or conditions such as common variable hypogammaglobulinemia Subjects on immunosuppressive medications such as azathioprine, mycophenolate mofetil, cyclosporine or require chronic corticosteroid use (defined as ? months of prednisone dose equivalent of ? mg). Immunosuppressive therapy, including: cyclosporine, antithymocyte globulin, or tacrolimus within months of study entry. Use of immunosuppressive therapy within days of starting study treatment. Immunosuppressive therapy includes but is not limited to cyclosporine A, tacrolimus, or high-dose corticosteroids. Subjects receiving corticosteroids must be at a dose level ? mg/day within days of initiating study treatment. Patients receiving cyclosporine A, tacrolimus, or sirolimus are not eligible for this study. Current treatment with sirolimus AND either cyclosporine or tacrolimus. Current, active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. History of organ transplant, or current active immunosuppressive therapy (such as cyclosporine, tacrolimus, etc.). Subjects requiring chronic use of immunosuppressive agents (eg, methotrexate, cyclosporine, corticosteroids) Patients who are expected to require any of the following therapies between enrollment and completion or discontinuation of the study treatment:\r\n* Immunosuppressive drugs, including corticosteroids, methotrexate, mercaptopurine, azathioprine, cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, ATG (anti-thymoglobulin), interleukin (IL)-receptor antibodies (basiliximab, daclizumab), tumor necrosis factor (TNF)-a antibodies (infiliximab, etanercept, adalimumab)\r\n* Radiotherapy for the target disease\r\n* Surgical therapy for the target disease Co-medication that may interfere with study results; e.g. immuno-suppressive agents other than corticosteroids, such as systemic cyclosporine and tacrolimus Current, active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. Treatment with chronic immunosuppressant (e.g., cyclosporine following transplantation) Patients must have failed at least two forms of immunosuppression:\r\n* Moderate-to-high dose corticosteroids (.- mg/kg/day**, and/or IV pulse methylprednisolone)\r\n** When cyclophosphamide is the accepted standard of care (renal and neurologic), the maximally tolerated dose of prednisone will be sufficient to meet the corticosteroid criterion\r\n* Azathioprine, methotrexate, cyclosporine, tacrolimus, belimumab, rituximab, or mycophenolate mofetil, in the case of severe and ongoing hemolytic anemia and/or thrombocytopenia, failure of intravenous immunoglobulin treatment will count as the second treatment Patient requires chronic use of immunosuppressive agents (e.g. methotrexate, cyclosporine) Patients must not require chronic use of immunosuppressive agents (e.g. methotrexate, cyclosporine) Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Treatment within days prior to enrollment with the following: cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, methotrexate, azathioprine, rapamycin, and targeted immune modulators such as abatacept (CTLA--Ig), adalimumab, alefacept, anakinra, belatacept (LEAY), efalizumab, etanercept, infliximab, or rituximab Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Known severe or life-threatening allergy or intolerance to ATG or cyclosporine/ tacrolimus Participants must be receiving systemic glucocorticoid therapy for cGVHD; all immunosuppressive therapy may include but not be limited to tacrolimus, sirolimus, CellCept, cyclosporine, and systemic corticosteroid must be at stable doses for days prior to the first cell infusion Any contraindication for GVHD prophylaxis with mycophenolate mofetil, cyclosporine A, or tacrolimus Current or planned use of immunomodulators including: infliximab, ?MP (mercaptopurine), methotrexate, cyclosporine, or other immunomodulatory drugs Any chronic medical condition requiring daily corticosteroids or other immunosuppressants (e.g. tacrolimus, sirolimus, cyclosporine, azathioprine, mycophenolate mofetil, etc.)