Tuning the correlation strength of electronic materials, to map out their phase diagrams, has led to the identification and classification of novel quantum phases, thereby elucidating the underlying physics [1]. The nature of such phase diagrams in the presence of nontrivial electronic topology represents a new frontier. After a general discussion of this background I will introduce a new state of matter, the Weyl-Kondo semimetal, discovered in a joint experimental [2,3] and theoretical [4,5] effort. I will present experiments on the heavy fermion material Ce3Bi4Pd3 [2], a semimetallic cousin of the well-known Kondo insulator Ce3Bi4Pt3. The strong spin-orbit coupling of the constituting elements together with the noncentrosymmetric and nonsymmorphic structure make this material a promising candidate to realize this new state. Indeed, our thermodynamic [2] and electrical transport [3] measurements evidence a highly unusual ``extreme topological response’’, which can be rationalized within the Weyl-Kondo semimetal picture [2-5]. I will furthermore show how this new state of matter transforms under the action of magnetic field [6], and close by highlighting the potential of such tuning studies for future discovery [7].