We discuss the validity of the naive Ward-Takahashi identities and trace identities for arbitrary n-point functions (n-pf's) of scalar, pseudoscalar, vector, and axial-vector currents and the improved energy-momentum tensor, thus extending the previous investigations in a unified way. We show that the validity of the naive Ward-Takahashi identities of the energy-momentum tensor implies the satisfaction of those of the vector currents. This removes an ambiguity concerning the minimal sets of anomalous current Ward-Takahashi identities. We find that all the anomalous Ward-Takahashi identities for the broad structure of n-pf's are again restricted to the axial-vector current of n- pf's of abnormal parity in a well-defined pattern, and the trace identity anomalies occur only in normal-parity n-pf's. We give all these anomalies. Our results show that there are no new anomalies associated with the inclusion of the energy-momentum tensor in the n-pf's.