  Resolving faint galaxies in large volumes is critical for accurate cosmic
reionisation simulations. While less demanding than hydrodynamical simulations,
semi-analytic reionisation models still require very large N-body simulations
in order to resolve the atomic cooling limit across the whole reionisation
history within box sizes $\gtrsim 100 \, h^{-1} {\rm Mpc}$. To facilitate this,
we extend the mass resolution of N-body simulations using a Monte Carlo
algorithm. We also propose a method to evolve positions of Monte Carlo halos,
which can be an input for semi-analytic reionisation models. To illustrate, we
present an extended halo catalogue that reaches a mass resolution of
$M_\text{halo} = 3.2 \times 10^7 \, h^{-1} \text{M}_\odot$ in a $105 \, h^{-1}
{\rm Mpc}$ box, equivalent to an N-body simulation with $\sim 6800^3$
particles. The resulting halo mass function agrees with smaller volume N-body
simulations with higher resolution. Our results also produce consistent
two-point correlation functions with analytic halo bias predictions. The
extended halo catalogues are applied to the \textsc{meraxes} semi-analytic
reionisation model, which improves the predictions on stellar mass functions,
star formation rate densities and volume-weighted neutral fractions. Comparison
of high resolution large volume simulations with both small volume or low
resolution simulations confirms that both low resolution and small volume
simulations lead to reionisation ending too rapidly. Lingering discrepancies
between the star formation rate functions predicted with and without our
extensions can be traced to the uncertain contribution of satellite galaxies.
