Previous studies of young stellar objects (YSOs) have uncovered a number of associated parsec-scale optical outflows, the majority of which are driven by low-mass, embedded Class I sources. Here we examine more evolved Classical T Tauri stars (CTTSs), i.e. Class II sources, to determine whether these are also capable of driving parsec-scale outflows. Five such sources are presented here - CW Tau, DG Tau, DO Tau, HV Tau C and RW Aur, all of which show optical evidence for outflows of the order of 1 pc (24' at the distance of Taurus-Auriga). These sources were previously known only to drive "microjets" or small-scale outflows less than or similar to1' in length. A parsec-scale outflow from a less evolved source (DG Tau 13) which was noted in the course of this work is also included here. Examination of the five newly discovered large-scale outflows from CTTSs shows that they have comparable morphologies, apparent dynamical timescales and degrees of collimation to those from less evolved sources. There is also strong evidence that these outflows have blown out of their parent molecular clouds. Finally we note that the "fossil record" provided by these outflows suggests their sources could have undergone FU Orionis-type outbursts in the past.