The far-infrared vibration-rotation-tunneling spectrum of (D2O)(4) has been measured in the spectral region near 2.04 THz. Observation of additional transition doublets with a constant 5.6 MHz spacing in a parallel (c-type) spectrum extends the first detailed study of this cluster [Science 271, 59 (1996)]. Three possibilities are explored for the origin of this small splitting : tunneling between degenerate equilibrium structures via facile torsional motions analogous to those observed in the water trimer, tunneling between nondegenerate structural frameworks, and tunneling made feasible only through excitation of a specific vibrational coordinate. The degenerate tunneling scheme best accounts for the spectral features, although the precise dynamics responsible for the observed spectral features cannot be uniquely established from the present data. A further doubling of spectral features, observed only in the K=2 manifold of transitions for J greater than or equal to 3, is symmetric about the unperturbed symmetric top energy levels and shows an approximate J(2) dependence of the spacing. The origin of these additional splittings, which are shown to be present in both upper and lower vibrational states of the spectrum, is likely to be due to an interaction between overall rotational angular momentum and the type of internal motion ("pseudorotation") that gives rise to a manifold of low energy states in water trimer. The measured interoxygen separations in (D2O)(n) (n=2,3,4,5) are analyzed in order to quantify the contribution of many-body forces in bulk water. An exponential contraction of this property toward the value found in ordered ice is observed.