We present results from neutral hydrogen (HI) observations of the tip of the Magellanic Stream (MS), obtained with the Arecibo telescope as a part of the on-going survey by the Consortium for Galactic studies with the Arecibo L-band Feed Array. We find four large-scale, coherent HI streams, extending continously over a length of 20 degrees, each stream possessing different morphology and velocity gradients. The newly discovered streams provide strong support for the tidal model of the MS formation by Connors et al. (2006), which suggested a spatial and kinematic bifurcation of the MS. The observed morphology and kinematics suggest that three of these streams could be interpreted as a 3-way splitting of the main MS filament, while the fourth stream appears much younger and may have originated from the Magellanic Bridge. We find an extensive population of HI clouds at the tip of the MS. Two thirds of clouds have an angular size in the range 3.5--10. We interpret this as being due to thermal instability, which would affect a warm tail of gas trailing through the Galactic halo over a characteristic timescale of a few Myrs to a few hundred Myrs. We show that thermal fragments can survive in the hot halo for a long time, especially if surrounded by a <10^6 K halo gas. If the observed clumpy structure is mainly due to thermal instability, then the tip of the MS is at a distance of ~70 kpc. A significant fraction of HI clouds at the tip of the MS show multi-phase velocity profiles, indicating the co-existence of cooler and warmer gas.