The configuration interaction (CI) method is used in the investigation into the properties of positron binding with a model alkali atom. Large CI calculations are necessary in order to obtain an accurate picture of the system. The implementation of optimized numerical software and parallelization made the systematic computation of the first excited state of the positronic alkali atoms possible. In addition to investigating the ground state properties of positronic alkali atoms, and the excited state properties of positronium, this is the first in depth investigation into the systematics of excited state positronic atoms. We show that the convergence properties of the first excited state (_P°) are slowly converging with respect to the radial and orbital basis. Expectation values and transition matrix elements are computed and extrapolated to the complete basis set limit. These calculations demonstrate that many atoms may have at least two bound positronic states that may be experimentally accessed using photons.