We combine the power of two stream-searching tools, STREAMFINDER and StarGO applied to the Gaia EDR3 data, to detect stellar debris belonging to the Cetus stream system that forms a complex, nearly polar structure around the Milky Way. In this work, we find the southern extensions of the northern Cetus stream as the Palca stream and a new southern stream, which overlap on the sky but have different distances. These two stream wraps extend over more than similar to 100 degrees on the sky (-60 degrees < delta < +40 degrees). The current N-body model of the system reproduces both as two wraps in the trailing arm. We also show that the Cetus system is confidently associated with the Triangulum/Pisces, Willka Yaku, and the recently discovered C-20 streams. The association with the ATLAS-Aliqa Uma stream is much weaker. All of these stellar debris are very metal-poor, comparable to the average metallicity of the southern Cetus stream with [Fe/H] = -2.17 +/- 0.20. The estimated stellar mass of the Cetus progenitor is at least 10(5.6) M (circle dot), compatible with Ursa Minor or Draco dwarf galaxies. The associated globular cluster with similar stellar mass, NGC 5824 very possibly was accreted in the same group infall. The multi-wrap Cetus stream is a perfect example of a dwarf galaxy that has undergone several periods of stripping, leaving behind debris at multiple locations in the halo. The full characterization of such systems is crucial to unravel the history of the assembly of the Milky Way, and importantly, to provide nearby fossils to study ancient low-mass dwarf galaxies.