Recently Francisco Presas Mata constructed the first examples of closed contact manifolds of dimension larger than 3 that contain a plastikstufe, and hence are non-fillable. Using contact surgery on his examples we create on every sphere S2n-1, n>1, an exotic contact structure ξ- that allows us to embed a plastikstufe. As a consequence, every closed contact manifold M (with exception of S1) can be converted by taking the connected sum of (M,ξ)# (S2n-1,ξ-) into a contact manifold that is not (semi-positively) fillable.