  Adding interactions to many-body Hamiltonians of geometrically frustrated
lattices often leads to diminished subspaces of localized states. In this
paper, we show how to construct interacting many-body Hamiltonians, starting
from the non-interacting tight-binding Hamiltonians, that preserve or even
expand these subspaces. The methods presented involve modifications in the
one-body network representation of the many-body Hamiltonians which generate
new interacting terms in these Hamiltonians. The subspace of many-particle
localized states can be preserved in the interacting Hamiltonian, by projecting
the interacting terms onto the subspace of many-body extended states or by
constructing the interacting Hamiltonian applying origami rules to the network.
Expanded subspaces of localized states are found if interacting terms that mix
subspaces with different number of particles are introduced. Furthermore, we
present numerical methods for the determination of many-body localized states
that allows one to address larger clusters and larger number of particles than
those accessible by full diagonalization of the interacting Hamiltonian. These
methods rely on the generalization of the concept of compact localized state in
the network. Finally, we suggest a method to determine localized states that
use a considerable fraction of the network.
