The influence of dynamic interlayer interactions on the spin-torque-driven and damped excitations are illustrated for a three layermacrospin model system that corresponds to a standard spin-torque oscillator. The free layer and a synthetic antiferromagnetic (SyF) pinned layer of the spin-torque oscillator are in-plane magnetized. In order to understand experimental results, numerical simulations have been performed considering three types of interlayer interactions: exchange interaction between the two magnetic layers of the SyF, mutual spin torque between the top layer of the SyF and the free layer and dipolar interaction between all three magnetic layers. It will be shown that the dynamic dipolar coupling plays a predominant role. First, it leads to a hybridization of the free layer and the SyF linear modes and through this gives rise to a strong field dependence of the critical current. In particular, there is a field range of enhanced damping in which much higher current is required to drive the modes into steady state. This results in a gap in the excitation spectrum. Second, the dynamic dipolar interaction is also responsible for the non-linear interaction between the current driven steady state mode and the damped modes of the system. Here one can distinguish: (i) a resonant interaction that leads to a kink in the frequency-field and frequency-current dispersions accompanied by a small hysteresis and a reduction of the linewidth of the steady state mode and (ii) a non-resonant interaction that leads to a strong frequency redshift of the damped mode. The results underline the strong impact of interlayer coupling on the excitation spectra of spin-torque oscillators and illustrate in a simple threemode model system how in the non-linear regime the steady state and damped modes influence each other.