4Hb-TaS2 is a transition metal dichalcogenide (TMD) with alternating single layers of H and T structure. Interestingly, these two building blocks have dramatically different bulk properties. While H is metallic and becomes superconducting at low temperature, the T structure has nearly flat bands that undergo a Mott transition below ~200K, stemming from a star-of-David CDW that sets in at higher temperature. Albeit this charge localization the T compound shows no sign of magnetic ordering and was recently proposed to be a gapless spin liquid. Thus, the 4Hb structure naturally combines itinerant electrons interacting with electrons on the brink of localization, possibly in highly exotic phases. Recent muon relaxation experiments reported signatures of chiral superconductivity in this compound. However, a large T-linear specific heat was also measured at lowest temperatures. In this talk I will propose a theoretical picture capturing the unusual phenomenology in this system. First, based on DFT calculations of the band structure, I will show that local moments couple to the many Fermi surfaces in the H layers with varying strengths when they appear in the T-layers. I will then present a model of multiband superconductivity with band dependent coupling to magnetic impurities, and show how such a model naturally reproduces the T-linear specific heat. Then I will discuss the implications of such a model to Kondo lattice physics in this system. If time permits, I will show how a similar model emerges in TMD bilayers subject to a moire superlattice potential.