Other mesoscopic modeling approaches employ much simpler potentials, more suitable for highly coarse-grained levels, in the form of single repulsive potentials. These potentials have roots in Flory-Huggins theory and self-consistent field theory in polymer physics. A prominent technique in this domain is Dissipative Particle Dynamics (DPD). DPD is a coarse-grained method that represents groups of atoms as single particles interacting through soft quadratic potentials, efficiently capturing hydrodynamic behavior. Another approach involves the Gaussian potential or the Gaussian Core Model (GCM), first introduced by in the study of fluid and solid phases. Compared with DPD, GCM introduces a dimension for the bead size, enhancing its versa-tility and applicability. In recent years, mesh-based density methods have emerged. Although the particles interact via density functionals in these methodologies, they essentially adopt soft-core potentials. For example, the MC-SCF and MD-SCF methods mimic the quadratic potentials in DPD, while the Hamiltonian hybrid particle-field (HhPF) method, which employs Gaussian filters within a mesh, resembles the Gaussian core model. Soft potentials generally improve phase space sampling efficiency by simplifying and smoothing energy landscapes, but efficiency may still be limited in some cases. For instance, soft interactions can cause systems to get stuck in a local configuration or enter into a state that resembles a glass transition due to kinetic slowdown and reduced mobility, especially at low temperatures and high densities. To observe phase coexistence in a model, both attractive and repulsive components must be present in the microscopic interactions. Existing implementations, which only carry the repulsion, are suitable for dense and homogeneous systems, but cannot handle liquid-gas coexistence and lose fine-structure control. Recent progress has been made to address these limitations. The many-body DPD (MDPD) method introduces a density-dependent attractive term into a conservative force, enabling the formation of vapor-liquid coexistence. For the MD-SCF, recent work introduces new equations of state (EOS). Sevink et al. proposed a modified Hamiltonian for the hybrid particle-field (hPF) method that replaces the usual compressibility term with terms that include higher-order density contributions in the EOS. This change in the Hamiltonian is argued to be necessary to achieve phase coexistence. Another inspiring development comes from the Gaussian core side. The Multi-Gaussian Core Model (MGCM) can introduce both positive and attractive components, enabling the study of interface problems and complex systems. They can also approximate targeting potentials, which is favorable in machine learning algorithms. Recently, we demonstrated how the HhPF is in principle equivalent to any two-body potential, depending only on the choice of the filter function. Continuing on this development line, this paper implements multiple Gaussian filters to reproduce the improvements accessible to the MGCM method, showing that it is possible to capture the essence of multi-phase fluid behavior by utilizing only an optimal choice of the filter function.