Classical microcontact printing and polymer pen lithography (PPL) involve ink transfer to substrates using solid elastomeric stamps. Ink depletion thus limits the number of successive stamping steps without reinking. Porous stamps developed to overcome this limitation are used only for manual proof‐of‐principle experiments. Here, porous composite stamps for scanner‐based capillary stamping (SCS) that can be mounted on automated printing devices designed for PPL are developed. Porous SCS composite stamps consist of a rigid controlled porous silica glass (CPG) layer and a porous polymeric stamping layer. The latter can be topographically structured with contact elements by replication molding. The mechanical stabilization by the CPG layer ensures that the contact elements are coplanar. SCS allows automated, continuous, high‐throughput patterning enabled by ink supply through the porous SCS composite stamps. Even after more than 800 consecutive stamp–substrate contacts without reinking (the porous SCS composite stamps themselves are used as ink reservoirs), ink microdroplets are deposited without deterioration of the pattern quality. However, SCS also allows supply of additional ink during ongoing stamping operations through the pore systems of the porous SCS composite stamps. ... mehrSCS can easily be adapted for multi‐ink patterning and may pave the way for further upscaling of contact lithography.