We investigate limits on the current of the PSI Injector II high intensity separate-sector isochronous cyclotron, in its present configuration and after a proposed upgrade. Accelerator Driven Subcritical Reactors, neutron and neutrino experiments, and medical isotope production all benefit from increases in current, even at the ∼10% level: the PSI cyclotrons provide relevant experience. As space charge dominates at low beam energy, the injector is critical. Understanding space charge effects and halo formation through detailed numerical modelling gives clues on how to maximise the extracted current. Simulation of a space-charge dominated low energy high intensity (9.5 mA DC) machine, with a complex collimator set up in the central region shaping the bunch, is not trivial. We use the OPAL code, a tool for charged-particle optics calculations in large accelerator structures and beam lines, including 3D space charge. We have a precise model of the present (production) Injector II, operating at 2.2 mA current. A simple model of the proposed future (upgraded) configuration of the cyclotron is also investigated. We estimate intensity limits based on the developed models, supported by fitted scaling laws and measurements. We have been able to perform more detailed analysis of the bunch parameters and halo development than any previous study. Optimisation techniques enable better matching of the simulation set-up with Injector II parameters and measurements. We show that in the production configuration the beam current scales to the power of three with the beam size. However, at higher intensities, 4th power scaling is a better fit, setting the limit of approximately 3 mA. Currents of over 5 mA, higher than have been achieved to date, can be produced if the collimation scheme is adjusted.