Multiple-satellite measurements of magnetic field and/or energetic particles during four magnetospheric substorms are presented. The data were obtained from Ogo 5 and Vela 4A, located near local midnight at about the same distance form the neutral sheet but separated by 3--10 RE in the radial direction. The substorm expansion phases all had multiple onsets, typically observed as multiple bursts of Pi 2 magnetic pulsations (which we use for accurate timing of each onset), auroral zone bay intensifications, and low-latitude positive bay increases. A minimum in the plasma sheet thickness was probably formed at Xsm~-15 RE in association with the formation of an X-type neutral line. Earthward of this line, successive substorm onset signatures were observed in an almost one-one relationship with ground Pi bursts: a short (~5 min) burst of magnetic fluctuations confined to the plasma sheet, a plasma sheet expansion, and a field vector rotation toward a more dipolar orientation. These onsets, which occurred at 10- to 15-min intervals, may have been caused by impulsive enhancements of field line reconnection. Since the plasma sheet was thinning before each new onset, it appears that these enhancements were triggered in the tail each time the plasma sheet became very thin, causing a disruption of the cross-tail electric currents. In the tailward part of the plasma sheet (Xsm~-18 RE) the plasma sheet was thinning down or remained thin until well after the last near-earth expansion, when a recovery occurred. The near-tail observations are consistent with a model in which the associated tailward motion of the neutral line started when the reconnection rate exceeded the earthward flux return rate, producing a tailward pressure which forced the neutral line to move tailward. A comparison with what appears to be a 'contracted oval substorm' shows that, even though this substorm apparently took place within a more limited local time sector, it had all the usual substorm features in the tail.