We report new multistriped phases at high densities in a three-state model (Si = 0, ± 1) driven by an external field E and influenced by repulsive nearest neighbor interactions. The dynamics are dictated by local Metropolis rates with the ratio of particle-particle to particle-hole exchange given by γ. In the noninteracting limit, this model shows an ordered, low-current phase above a density-dependent critical field. In this phase the two types of charges are segregated from each other and from the vacancies, forming stripes transverse to the field direction. Addition of a repulsive bilinear interaction J favors mixing of the charges. This interaction competes directly with the charge-segregated ordering and the system undergoes a nonequilibrium transition to one of four other types of striped phases, some with checkerboard ordering. We have calculated the staggered charge density and used the amplitude of its longest wavelength Fourier component along the field direction as an order parameter to characterize this new type of striped ordering. The phase diagram in the parameter space of E, J, γ, and density shows both first and second order transitions, with second order transitions most prevalent in the high-E/J, high density regions. Our study also shows a reentrant phase diagram with only second order transitions for high γ and a tricritical topology at low γ. For field strengths close to zero, the system orders in a checkerboard fashion above a J-dependent density. Results were obtained using Monte Carlo simulations on a 30×30 square lattice with periodic boundary conditions and charge conservation.