The local operators of a unitary 4d N=2 SCFT in twisted Schur cohomology form a vertex operator algebra (VOA). By "local operator" we mean one associated with a point in space-time. We show that to every 4d N=2 SCFT there is associated a vertex algebra containing the VOA of local twisted Schur operators as a proper subalgebra. The new vertex operators of this larger vertex algebra are associated with certain extended operators (line, surface, etc.) in twisted Schur cohomology. Though we can compute some partial results in simple SCFTs, the structure of these extended vertex algebras is still largely mysterious.