Thermodynamics of the Kitaev honeycomb magnet α-RuCl3 is studied for different directions of in-plane magnetic field using measurements of the magnetic Grüneisen parameter ΓB and specific heat C. We identify two critical fields BcAF1 and BcAF2 corresponding, respectively, to a transition between two magnetically ordered states and the loss of magnetic order toward a quantum paramagnetic state. The BcAF2 phase boundary reveals a narrow region of magnetic fields where inverse melting of the ordered phase may occur. No additional transitions are detected above BcAF2 for any direction of the in-plane field, although a shoulder anomaly in ΓB is observed systematically at 8-10T. Large field-induced entropy effects imply additional low-energy excitations at low fields and/or strongly field-dependent phonon entropies. Our results establish universal features of α-RuCl3 in high magnetic fields and challenge the presence of a field-induced Kitaev spin liquid in this material.