The linear-response theory of the multiconfigurational time-dependent Hartree for bosons method (LR-MCTDHB) for computing many-body excitations of trapped Bose-Einstein condensates [Phys. Rev. A 88, 023606 (2013); J. Chem. Phys. 140, 034108 (2014)] is implemented, for the first time, for systems with general interparticle interaction. This allows us to investigate the many-body excitation spectrum of interacting bosons with, for instance, a long-range interaction. Illustrative numerical examples for repulsive and attractive bosons are provided. The LR-MCTDHB theory is capable of identifying all excitations, including the excitations which are not unraveled within Bogoliubov-de Gennes equations. The theory is herewith benchmarked against the exactly-solvable one-dimensional harmonic-interaction model. As a complementary result, using a complex transformation, we represent LR-MCTDHB in a compact block-diagonal form, opening up thereby an avenue for treating larger many-body systems. We expect the LR-MCTDHB theory and its implementation for general interparticle interaction to provide a proved probe into the many-body excitations involved in the out-ofequilibrium dynamics of trapped interacting bosons.