The present invention provides vectors that comprise a polynucleotide encoding an chimeric antigen recognizing receptor and a polynucleotide encoding a chimeric costimulatory receptor that recognizes a second antigen. T cells comprising the vector may have greater activity against cells positive for both antigens. Methods of using the immunoresponsive cell include those for the treatment of neoplasia and other pathologies where an increase in an antigen-specific immune response is desired.