The primary motivation of the GlueX experiment is to search for and ultimately study the pattern of gluonic excitations in the meson spectrum produced in gamma p collisions. Recent lattice QCD calculations predict a rich spectrum of hybrid mesons that have both exotic and non-exotic JPC, corresponding to q q-bar (q=u, d, or s) states coupled with a gluonic field. A thorough study of the hybrid spectrum, including the identification of the isovector triplet, with charges 0 and +-1, and both isoscalar members, |s s-bar> and |u u-bar> + |d d-bar>, for each predicted hybrid combination of JPC, may only be achieved by conducting a systematic amplitude analysis of many different hadronic final states. We propose the development of a kaon identification system, supplementing the existing GlueX forward time-of-flight detector, in order to cleanly select meson and baryon decay channels that include kaons. Once this detector has been installed and commissioned, we plan to collect a total of 200 days of physics analysis data at an average intensity of 5 x 10^7 tagged photons on target per second. This data sample will provide an order of magnitude statistical improvement over the initial GlueX data set and, with the developed kaon identification system, a significant increase in the potential for GlueX to make key experimental advances in our knowledge of hybrid mesons and Cascade baryons.