Two-dimensional(2D) materials are among the most promising candidatesfor beyond-silicon electronic, optoelectronic, and quantum computingapplications. Recently, their recognized importance sparked a pushto discover and characterize novel 2D materials. Within a few years,the number of experimentally exfoliated or synthesized 2D materialswent from a few to more than a hundred, with the number of theoreticallypredicted compounds reaching a few thousand. In 2018 we first contributedto this effort with the identification of 1825 compounds that areeither easily (1036) or potentially (789) exfoliable from experimentallyknown 3D compounds. Here, we report on a major expansion of this 2Dportfolio thanks to the extension of the screening protocol to anadditional experimental database (MPDS) as well as the updated versionsof the two databases (ICSD and COD) used in our previous work. Thisexpansion leads to the discovery of an additional 1252 monolayers,bringing the total to 3077 compounds and, notably, almost doublingthe number of easily exfoliable materials to 2004. We optimize thestructural properties of all these monolayers and explore their electronicstructure with a particular emphasis on those rare large-bandgap 2Dmaterials that could be precious in isolating 2D field-effect-transistorchannels. Finally, for each material containing up to 6 atoms perunit cell, we identify the best candidates to form commensurate heterostructures,balancing requirements on supercell size and minimal strain.