One of the most widely used current sheet models is the Harris equilibrium, which is part of a broader class of solutions known as the isotropic current sheets. The Harris solution is characterized by the ratio of ion-to-electron cross-field drift speeds which is solely determined by their temperature ratio. Thus, one cannot have a situation where one species drifts faster than the other in one region, while the role is reversed in the other region. However, observations and simulations indicate that thin current sheet is often characterized by dominant electron current layer embedded in a thicker plasma sheet. In general, in typical diamagnetic current sheets with higher ion temperature, the ions are usually the dominant current carriers. The present talk is concerned with a possible generalization of Harris solution to a model where either the electron- or ion-dominated thin current layer is embedded within thicker current sheet dominated by the other species. The importance of the present work is in the context of magnetic reconnection. The ion-dominated current sheet may be susceptible to the excitation of the modified-two-stream instability (MTSI) at the center of the neutral sheet, thereby providing the anomalous resistivity. In contrast, the customary Harris model is unstable to the lower-hybrid-drift instability (LHDI) which is excited only at the outer edge of the current sheet, and thus is incapable of directly influencing the neutral sheet dynamics. The scenario of MTSI excited near the neutral sheet in ion-dominated non-Harris model may be consistent with laboratory magnetic reconnection experiment (MRX) where high-frequency electromagnetic fluctuations have been directly measured at the neutral sheet.