  Low-lying baryon resonances have been explored using Hamiltonian Effective
Field Theory (HEFT), in a formalism where resonances with a three-quark
component are described by both two-particle meson-baryon states and a bare
basis state. Here, we investigate the use of multiple bare states in the
Hamiltonian, to extend the formalism to higher energy ranges, and represent a
larger portion of the low-lying baryon spectrum. Introducing a second bare
state into a toy model extension of the low-energy $\Delta(1232)$ system, we
explore the influence of the second bare state on the position of poles in the
infinite-volume $T$-matrix. Considering the same system in a finite-volume, we
analyse the finite-volume energy spectrum in the presence of a second bare
state, providing insight into the interplay between two bare basis states,
representing quark-model states, and the relationship between infinite-volume
poles and finite-volume eigenstates.
