Parametric instabilities are dynamical instabilities arising when the mechanical state of a structure is properly modulated in time. It is sometimes seen as a phenomenon to avoid for example with sailing ships (parametric rolling) but it has also been exploited in vibrating fluids (Faraday waves) or NanoElectroMechanical Systems (parametric amplification). One well-known limitation in fully exploiting classic parametric instabilities based on small periodic modulation of a mechanical state is that inherent friction forces rapidly cancel sub-harmonic parametric resonances. To overcome this drawback, we suggest to formerly modify the state of a mechanical system close to its diverging instability, so that it becomes possible to periodically modulate a system between a naturally oscillating and diverging state. This original way of enhancing and controlling parametric instabilities is illustrated here through the numerical and experimental implementation of an electromagnetic pendulum. Not only we find it is possible to greatly enhance the number of subharmonic instability regions, but it is feasible to control the width of those regions, opening a promising way for frequency filtering in NanoElectroMechanical Systems.