The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.