Conventional approaches to generating and distributing entangled quantum states usually rely on bulky traditional optical devices, posing significant challenges to system miniaturization and integration. Here we report an entanglement engineering scheme that utilizes quantum interference on a metasurface, combined with postselection, to generate and distribute multiple polarization-entangled photon pairs. Two unentangled identical photons, differing only in polarization, are incident on a multichannel metasurface where each channel supports a specific polarization transformation. The metasurface facilitates two-photon interference, generating postselected polarization-entangled states and forming a fully connected entanglement distribution among every two output channels. Experiments demonstrate the generation and distribution of four Bell states across 21 channel pairs, underscoring the potential of metasurfaces as compact, scalable entanglement sources for quantum networking.