We present a comprehensive study of traversable wormholes in multi-metric gravity, a ghost-free theory with N interacting metric tensors. The action, field equations, and constraints are derived step by step. We construct a static, spherically symmetric wormhole ansatz with a Gaussian deformation localised at the throat, and reduce the field equations to a system of ordinary differential equations. A central result is a no-horizon theorem: any stationary, asymptotically flat solution with a non-zero multi-metric charge Q, defined as the asymptotic flux of a conserved current built from the metric differences, cannot contain a Killing horizon and must therefore be a traversable wormhole. We show analytically and numerically that the null energy condition (NEC) violation is suppressed by a factor 1/N compared to the single-metric case, and that the exotic matter can be confined to an arbitrarily narrow shell. The deflection angle and Shapiro time delay are computed, and the stability under radial perturbations is analysed. The model satisfies Solar System constraints and makes falsifiable predictions for near-future instruments.