We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be written as a sum of N-body {delta}-interactions, and then considering general contact potentials. Results for the quasi-particle spectrum and the stability are presented. We then examine non-local interactions, focusing on two different cases of 3-body non-local interactions. Our results are used for systems with 2- and 3-body {delta}-interactions and applied for realistic values of the trap parameters. Finally, the effect of conservative 3-body terms in dipolar systems and soft-core potentials (that can be simulated with Rydberg dressed atoms) is also studied.
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