The identification and localization of proteins and other biomolecules, throughout entire brain circuits, with nanoscale precision would enable many fundamental insights into the mechanisms underlying the operation of normal and pathological neural networks. We recently discovered that we could physically magnify specimens by embedding them in a dense swellable polymer, anchoring key biomolecules to the polymer mesh, and adding water to swell the polymer, a process we call ‘expansion microscopy’ (ExM; Science 347(6221):543-548). Despite the high isotropy of the expansion process, the initial polymer recipe enabled just 4-4.5x expansion, or roughly 60-70 nm spatial resolution. Ideally it would be possible to improve the expansion chemistry so as to enable, ultimately, the imaging of membrane boundaries, as well as protein complexes. Here, we report on a next-generation ExM chemistry that can achieve ~15-20x physical magnification of mouse brain tissues, or 20-nm lateral resolution on conventional optical microscopes. As with the first version of ExM, next-generation ExM-processed samples are optically clear. Thus, next-generation ExM may be useful for imaging nanoscale neuronal structures such as synaptic clefts or synaptic vesicles over entire neural circuits in intact mammalian tissues. Brain circuit mapping using next-generation ExM may open up a variety of insights into the underpinnings of behavior, cognition, and disease. We continue to refine the chemistry and to explore how affinity tags can be adapted to work in this new expanded environment.