The production of multiple Higgs bosons at the CERN LHC provides a direct way to measure the trilinear and quartic Higgs self-interaction strengths as well as potential access to beyond the standard model effects that can enhance production at large transverse momentum $p_{\mathrm{T}}$. The largest event fraction arises from the fully hadronic final state in which every Higgs boson decays to a bottom quark-antiquark pair ($b\bar{b}$). This introduces a combinatorial challenge known as the \emph{jet assignment problem}: assigning jets to sets representing Higgs boson candidates. Symmetry-preserving attention networks (SPA-Nets) have been been developed to address this challenge. However, the complexity of jet assignment increases when simultaneously considering both $H\rightarrow b\bar{b}$ reconstruction possibilities, i.e., two "resolved" small-radius jets each containing a shower initiated by a $b$-quark or one "boosted" large-radius jet containing a merged shower initiated by a $b\bar{b}$ pair. The latter improves the reconstruction efficiency at high $p_{\mathrm{T}}$. In this work, we introduce a generalization to the SPA-Net approach to simultaneously consider both boosted and resolved reconstruction possibilities and unambiguously interpret an event as "fully resolved'', "fully boosted", or in between. We report the performance of baseline methods, the original SPA-Net approach, and our generalized version on nonresonant $HH$ and $HHH$ production at the LHC. Considering both boosted and resolved topologies, our SPA-Net approach increases the Higgs boson reconstruction purity by 57--62\% and the efficiency by 23--38\% compared to the baseline method depending on the final state.