Expenses associated with shipping, installation, land, regulatory compliance and on-going maintenance and operations of utility-scale photovoltaics can be significantly reduced by increasing the power conversion effciency of solar modules(1) through improved materials, device designs and strategies for light management(2-4). Single-junction cells have performance constraints defined by their Shockley-Queisser limits(5). Multijunction cells(6-12) can achieve higher effciencies, but epitaxial and current matching requirements between the single junctions in the devices hinder progress. Mechanical stacking of independent multi-junction cells(13-19) circumvents these disadvantages. Here we present a fabrication approach for the realization of mechanically assembled multi-junction cells using materials and techniques compatible with large-scale manufacturing. The strategy involves printing-based stacking of microscale solar cells, sol-gel processes for interlayers with advanced optical, electrical and thermal properties, together with unusual packaging techniques, electrical matching networks, and compact ultrahigh-concentration optics. We demonstrate quadruple-junction, four-terminal solar cells with measured effciencies of 43.9% at concentrations exceeding 1,000 suns, and modules with effciencies of 36.5%.