Constructing higher-order vesicle assemblies has discipline-spanning potential from responsive soft-matter materials to artificial cell networks in synthetic biology. This potential is ultimately derived from the ability to compartmentalise and order chemical species in space. To unlock such applications, spatial organisation of vesicles in relation to one another must be controlled, and techniques to deliver cargo to compartments developed. Herein, we use optical tweezers to assemble, reconfigure and dismantle networks of cell-sized vesicles that, in different experimental scenarios, we engineer to exhibit several interesting properties. Vesicles are connected through double-bilayer junctions formed via electrostatically controlled adhesion. Chemically distinct vesicles are linked across length scales, from several nanometres to hundreds of micrometres, by axon-like tethers. In the former regime, patterning membranes with proteins and nanoparticles facilitates material exchange between compartments and enables laser-triggered vesicle merging. This allows us to mix and dilute content, and to initiate protein expression by delivering biomolecular reaction components.