The generalized collective mode approach proposed for the investigation of time correlation functions of a dense fluid is now extended to higher-order approximations. The generalized collective mode spectra of a Lennard-Jones fluid have been calculated for longitudinal fluctuations up to the nine-mode description and also for transverse fluctuations up to the four-mode description using molecular dynamics. The results are obtained as functions of wave vector. For longitudinal fluctuations four new kinetic modes are found in addition to five modes known previously. For transverse fluctuations we found the generalized hydrodynamic and three kinetic modes. A comparison of previous works with the results of lower-order approximations has been made.