Embodiments of the disclosure concern methods and compositions for immunotherapy for diseases and malignancies associated with viruses other than HPV or with non-virus-associated diseases and malignancies, such as wherein the VST encodes a CAR specific for a non-viral cancer and the VST can be stimulated in vitro or in vivo using viruses, viral vaccines or oncolytic viruses. In specific embodiments, methods concern production of immune cells that target one or more antigens of HIV, EBV, CMV, adenovirus, vaccinia virus, and/or VZV, including methods with stimulation steps that employ IL-7 and IL-15, but not IL-2, IL-4, or both. Other specific embodiments utilize stimulations in the presence of certain cells, such as costimulatory cells and certain antigen presenting cells.