  We introduce MF-Box, an extended version of MFEmulator, designed as a fast
surrogate for power spectra, trained using N-body simulation suites from
various box sizes and particle loads. To demonstrate MF-Box's effectiveness, we
design simulation suites that include low-fidelity suites (L1 and L2) at $256
\,\mathrm{Mpc}/h$ and $100 \,\mathrm{Mpc}/h$, each with $128^3$ particles, and
a high-fidelity suite (HF) with $512^3$ particles at $256 \,\mathrm{Mpc}/h$,
representing a higher particle load compared to the low-fidelity suites. MF-Box
acts as a probabilistic resolution correction function, learning most of the
cosmological dependencies from L1 and L2 simulations and rectifying resolution
differences with just 3 HF simulations using a Gaussian process. MF-Box
successfully emulates power spectra from our HF testing set with a relative
error of $< 3\%$ up to $k \simeq 7 \,h/\mathrm{Mpc}$ at $z \in [0, 3]$, while
maintaining a cost similar to our previous multi-fidelity approach, which was
accurate only up to $z = 1$. The addition of an extra low-fidelity node in a
smaller box significantly improves emulation accuracy for MF-Box at $k > 2
\,h/\mathrm{Mpc}$, increasing it by a factor of $10$. We conduct an error
analysis of MF-Box based on computational budget, providing guidance for
optimizing budget allocation per fidelity node. Our proposed MF-Box enables
future surveys to efficiently combine simulation suites of varying quality,
effectively expanding the range of emulation capabilities while ensuring cost
efficiency.
