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In this work we introduce an integrable family of Hamiltonians describing dipolar bosons behavior disposed in an optical lattice. The models are very general, taking into account the single and double tunnelings of the particles in different geometrical configurations within the lattice, the intra and inter site interactions between them, and also considering the correlated hopping between sites. The models are derived through the Quantum Inverse Scattering Method, and admit exact solution by applying an extended algebraic Bethe Ansatz, in which a new set of pseudovacua are required to obtain a complete set of Bethe states. This new family of models is noteworthy due to its generality, being capable of describing not only interesting and new behavior, but also important models such as the Two-Site Bose-Hubbard model and, more recently, a three-site atomtronic switching device [K.W. Wilsmann et al., Commun. Phys. 1, 91 (2018)] can be obtained as a limiting case.