We systematically investigate the microstructures of metallic glasses with nanoscale networks of chemical heterogeneities introduced by the presence of a metastable miscibility gap, and their effects on modulating plastic flow of the alloys. Microstructural analysis of as-quenched alloys and the associated thermodynamic assessment in Cu-Zr-Al-Y metallic glass-forming system suggest that the existence of a metastable miscibility gap can induce not only phase-separated microstructures with sharp phase interfaces but also compositional fluctuations without a clear interface ranging from atomic scale to a few-nanometer scale in the fully amorphous alloys. The statistical analysis of shear avalanches in such compositionally heterogeneous metallic glasses reveals that chemical heterogeneities extending over a few nanometers promote a relatively large population of shear deformation units jammed before the nucleation of mature shear bands. This leads to the multiple nucleation of shear bands and sluggish deformation behavior along them. However, phase interfaces formed by phase separation inside the miscibility gap promote rapid propagation of shear bands at low flow stress, while compositional fluctuations creating non-sharp interfaces emerging at the outside of miscibility gap have relatively high resistance against shear band propagation. We hence suggest that the optimization of nanoscale compositional fluctuations in metallic glasses in terms of topology, percolation and magnitude can be an effective route for improving the materials' damage tolerance upon plastic flow.