The phase diagram of the filled skutterudite CeOs4Sb12 has been mapped in fields H of up to 60 T and temperatures T down to 0.5 K using resistivity, magnetostriction, and MHz conductivity. The valence transition separating the semimetallic, low-H, low-T , L phase from the metallic high-H, high-T H phase exhibits a very unusual, wedge-shaped phase boundary, with a non-monotonic gradient alternating between positive and negative. This is quite different from the text-book "elliptical" phase boundary usually followed by valence transitions. Analysis of Shubnikov-de Haas oscillations within the H phase reveals an effective mass that increases as H drops toward the H − L phase boundary, suggesting proximity to a quantum-critical point. The associated magnetic fluctuations may be responsible for the anomalous H, T dependence of the valence transition at high H, whereas the low−H, high−T portion of the phase boundary may rather be associated with the proximity of CeOs4Sb12 to a topological semimetal phase induced by uniaxial stress.