  We study the Extended Bose-Hubbard Model with a three-body onsite
interaction. Using an exact diagonalization method and a variational Matrix
Product States algorithm, \emph{Alps mps-optim}, we compute and analyse the
energy charge gap and finite system correlation functions to obtain the phase
boundaries and determine the phases and phase transitions of the model. For
\mbox{$\frac{V}{U} = 0.6$} and \mbox{$\frac{W}{U} = 0$}, we observed the
emergence of the Haldane insulator (HI) phase at the tip of the \mbox{$\rho =
1$} charge density wave (CDW) lobe and for \mbox{$\frac{V}{U} = 0.6$} and
\mbox{$\frac{W}{U} = 1$}, we observed the emergence of the supersolid (SS)
phase at the tip of the \mbox{$\rho = 1/2$} charge density wave (CDW) lobe. We
also noticed that the effect of the inclusion of both the three-body onsite and
nearest neighbor interactions on the phase diagram of the model for filling
factor \mbox{$\rho = 2$} is to stabilize the Mott insulator (MI) phase such
that the system remains in the MI phase for all values of $\frac{V}{U}$.
