Standard forms of nonlinear microscopy rely on single beam scanning, but the usually weaker signal and the need to image in real-time call for parallelization of the image formation. Since the nonlinear susceptibilities necessitate a comparatively large illumination power, with current laser systems the brightness or field of view of any parallelized nonlinear microscope is limited by the brightness of the laser. For example, by producing an array of high aperture foci, multifocal multiphoton microscopy (MMM) provides real-time, light-efficient three-dimensional fluorescence imaging at high-resolution. The available power limits the degree of parallelization and hence codetermines the field of view. As the utilization of all the laser power is imperative, the focal intensity can be adjusted only through altering the number of foci. This compromises to some extent the flexibility to adjust the focal intensity to benign and effective levels. Here we introduce space-multiplexing (SMX) as a novel option in parallelized nonlinear microscopy, which enables an improved exploitation of the total laser power and facilitates changing the intensity levels in selected regions, without attenuating the total laser power. The basic idea of SMX is to overlap arrays of slightly offset coherent focal fields whose interference modulates the intensity across the sample. For a given degree of parallelization and power, SMX increases the two- and three-photon excited signal of parallelized nonlinear microscopy by a factor of up to 1.5 and 2.5, respectively. To some extent, sensitive regions may be spared out, whereas in regions with weaker nonlinear susceptibilities the intensity is increased. SMX is relevant to all modes of nonlinear microscopy, including parallelized second- and third-harmonic imaging, coherent anti-Stokes Raman scattering, and wide field multiphoton excitation.