By investigating thoroughly the tunable behavior of coupled modes, we highlight how it provides new means to handle the properties of spin transfer nano-oscillators. We first demonstrate that the main features of the microwave signal associated with coupled vortex dynamics i.e. frequency, spectral coherence, critical current, mode localization, depends drastically on the relative vortex core polarities. Secondly we report a large reduction of the nonlinear linewidth broadening obtained by changing the effective damping through the control of the core configuration. Such a level of control on the nonlinear behavior reinforces our choice to exploit the microwave properties of collective modes for applications of spintronic devices in novel generation of integrated telecommunication devices.