The weakly bound diatomic systems He-4(2) and (HeH-)-He-4 have been found able to support only one bound state for J=0, although the latter also supports an additional bound state for J=1. In the present paper we, therefore, study the structure of the bound states which might exist for the weakly bound triatomic (He2H-)-He-4, in its J=0 state, by describing the full potential as a simple addition of two-body (2B) interactions. We carry out bound state calculations using both Jacobi coordinates within a discrete variable representation (DVR) and pair coordinates with a distributed Gaussian function (DGF) expansion. The system is shown to possess two bound states with respect to its lower dissociation threshold and two further "ghost" states before the complete break-up threshold. The spatial structures of such states and of the floppy complex are analyzed in detail, as is the possibility of detecting Efimov-type states in such a weakly bound aggregate. Finally, the inclusion of three-body (3B) forces in the description of the full interaction and its effect on the number of possible bound states is also discussed. (C) 2001 American Institute of Physics.