In order to understand the evolution of the protons and magnetic field in the inner plasma sheet from quiet to disturbed conditions, we incorporate a modified version of the Magnetospheric Specification Model (MSM) with a modified version of the Tsyganenko 96 (T96) magnetic field model to simulate the protons and magnetic field under an increasing convection electric field with two-dimensional (2-D) force balance maintained along the midnight meridian. The local time dependent proton differential fluxes assigned to the model boundary are a mixture of hot plasma from the mantle and cooler plasma from the low latitude boundary layer (LLBL). We previously used this model to simulate the inner plasma sheet under weak convection corresponding to a cross polar cap potential drop (ΔΦPC) equal to 26 kV and obtained 2-D quiet time equilibrium for proton and magnetic field that agrees well with observations. We start our simulation for enhanced convection with this quiet time equilibrium and time-independent boundary particle sources and increase ΔΦPC steadily from 26 to 146 kV in 5 hours. Simulations are also run separately to steady states by keeping ΔΦPC constant after it is increased to 98 and 146 kV. The magnitudes of proton pressure, number density, and temperature and their increase from quiet to moderate activity (ΔΦPC = 98 kV) are consistent with most observations. Our simulation at high activity (ΔΦPC = 146 kV) underestimates the observed pressure and temperature. This disagreement indicates possible dependence of the boundary particle sources on activity and possible effects of solar wind dynamic pressure enhancements that have not yet been included in our simulation. The simulated equatorial pressures and temperatures show stronger enhancement on the dusk side than on the dawn side as convection is increased, while density profiles show an increase on the dawn side and a decrease on the dusk side. The simulated proton flow speed at the equatorial plane increases with enhancing convection while the overall flow direction does not change significantly, a result of enhancement in both the earthward electric drift and the azimuthal diamagnetic drift. The equatorial magnetic field strength decreases more in the near-Earth plasma sheet than at larger radial distances as ΔΦPC increases, resulting in an increasing flat radial profile with enhancing convection. The feedbacks from diamagnetic drift and magnetic fields to increasing convection are found to restrain the pressure increase. Based on the good agreement between our results and observations at moderate activity, our magnetic field indicates that the plasma and magnetic field in the plasma sheet can be in a state far from possible force balance inconsistency during periods of moderately enhanced convection. A scale analysis of our results shows that the frozen-in condition E = -v ¿ B is not valid in the inner plasma sheet for moderate activity.