We theoretically and experimentally demonstrate a multifrequency excitation and detection scheme in apertureless near field optical microscopy, that exceeds current state of the art sensitivity and background suppression. By exciting the AFM tip at its two first flexural modes, and demodulating the detected signal at the harmonics of their sum, we extract a near field signal with a twofold improved sensitivity and deep sub-wavelength resolution, reaching λ=230. Furthermore, the method offers rich control over experimental degrees of freedom, expanding the parameter space for achieving complete optical background suppression. This approach breaks the ground for noninterferometric complete phase and amplitude retrieval of the near field signal, and is suitable for any multimodal excitation and higher harmonic demodulation.