We investigate the dynamics of Earth's quasi-parallel terrestrial bow shock based on measurements from the Magnetospheric MultiScale (MMS) spacecraft constellation during a period of near-radial interplanetary magnetic conditions, when the interplanetary magnetic field and the solar wind (SW) velocity are nearly anti-parallel. High-speed earthward ion flows with properties that are similar to those of the pristine SW are observed to be embedded within the magnetosheath-like plasma. These flows are accompanied by Interplanetary Magnetic Field (IMF) intensity of less than about 10 nT, compared to nearby magnetosheath intensities of generally greater than 10 nT. The high-speed flow intervals are bounded at their leading and trailing edges by intense fluxes of more energetic ions and large amplitude quasi-sinusoidal magnetic oscillations, similar to ultra-low frequency waves known to steepen and pileup on approach toward Earth to form the quasi-parallel bow shock. The MMS string-of-pearls configuration is aligned with the outbound trajectory and provides inter-spacecraft separations of several hundred km along its near 10³length, allowing sequential observation of the plasma and magnetic field signatures during the event by the four spacecraft. The SW-like interval is most distinct at the outer-most MMS-2 and sequentially less distinct at each of the trailing MMS spacecraft. We discuss the interpretation of this event alternatively as MMS having observed a quasi-rigid bow shock contraction/expansion cycle, ripples or undulations propagating on the bow shock surface, or a more spatially local evolution in the context of either a deeply deformed shock surface or a porous shock surface, as in the three-dimensional patchwork concept of the quasi-parallel bow shock, under the extant near-radial IMF condition.