CeRhIn5 is a prototypical antiferromagnetic heavy-fermion compound, whose behavior in a magnetic field is unique. A magnetic field applied in the basal plane of the tetragonal crystal structure induces two additional phase transitions. When the magnetic field is applied along, or close to, the c axis, a new phase characterized by a pronounced in-plane electronic anisotropy emerges at B * ≈ 30 T, well below the critical field, Bc 50 T, to suppress the antiferromagnetic order. The exact origin of this new phase, originally suggested to be an electronic-nematic state, remains elusive. Here we report low-temperature specific heat measurements in CeRhIn5 in high static magnetic fields up to 36 T applied along both the a and c axes. For fields applied along the a axis, we confirmed the previously suggested phase diagram, and extended it to higher fields. This allowed us to observe a triple point at ∼ 30 T, where the first-order transition from an incommensurate to commensurate magnetic structure merges into the onset of the second-order antiferromagnetic transition. For fields applied along the c axis, we observed a small but distinct anomaly at B * , which we discuss in terms of a possible field-induced transition, probably weakly first-order. We further suggest that the transition corresponds to a change of magnetic structure. We revise magnetic phase diagrams of CeRhIn5 for both principal orientations of the magnetic field based entirely on thermodynamic anomalies.