  We discuss modeling of nuclear structure beyond the 2-body interaction
paradigm. Our first example is related to the need of three nucleon contact
interaction terms suggested by chiral perturbation theory. The relationship of
the two low-energy effective coupling parameters for the relevant three nucleon
contact interaction terms $c_D$ and $c_E$ that reproduce the binding energy of
$^3$H and $^3$He has been emphasized and the physically relevant parameter
region has been illustrated using the binding energy of $^4$He. Further
justification of A-body interaction terms is outlined based on the
Okubo-Lee-Suzuki effective interaction method used in solving the nuclear
many-body problem within a finite model space. The third example we use is an
exactly solvable A-body extended pairing interaction applied to heavy nuclei
with a long isotopic chains, in particular using $^{132}$Sn and $^{208}$Pb as
closed core system illustrates a remarkable relationship between the extended
pairing strength $G(A)$ and the size of the valence space $\dim(A)$ for the
members of these two isotope chain: $G(A)=\alpha\dim(A)^{-\beta}$ with
$\alpha=259.436$ for Sn and $\alpha=366.77$ for Pb while the parameter $\beta$
is practically 1. These three cases present evidence for the need of better
understanding of the three-nucleon (NNN), four-nucleon (NNNN), and A-body
interactions in nuclei either derived from ChPT or from a phenomenological
considerations.
