Inherent limitations of the traditional time reversal process in the case of multiple sources or scatterers make it impossible to distinguish them individually. The selective source reduction (SSR) method employs a subtraction technique to selectively suppress in amplitude (and ideally eliminate) a time reversed focal signal that is masking another focus. In previous work, Scalerandi et al. and Anderson et al. successfully applied the SSR method to identify masked primary sources in a fully linear medium. Here, we extend the capabilities of the SSR method to deal with (i) secondary sources (for example, scattering caused by embedded defects) and (ii) nonlinear scattering generated during the ultrasonic wave propagation as well. We call this new method selective source reduction based on nonlinear time reversed acoustics (SSR-NLTRA). In the extended approach, the contribution of all primary sources is first eliminated by means of the scaling subtraction method. Subsequently, the SSR-TRA method is applied to the remaining nonlinear content of the signals. We show by means of two dimensional wave propagation simulations that the new method can be applied iteratively to successfully image multiple masked nonlinear defects.