We calculate the density profiles of a system of bosons with off-diagonal confinement and local interaction between two or three particles, using the density matrix renormalizaction group method. We found different ground-states: Mott insulator, superfluid and diverse mixed states. We observe that the Mott insulator lobes are surrounded by Mott insulator-superfluid coexistence state regardless the kind of the local interaction. The area of the Mott insulator lobes decreases for the two-body interactions and remain the same for three-body interactions.