Precision measurements of the magnetization and ac susceptibility of Cu2OSeO3 are reported for magnetic fields along different crystallographic directions, focusing on the border between the conical and the field-polarized state for a magnetic field along the (100) axis, complemented by selected specific heat data. Clear signatures of the emergence of a second skyrmion phase and a tilted conical phase are observed, as recently identified by means of small angle neutron scattering. The low-temperature skyrmion phase displays strongly hysteretic phase boundaries, but no dissipative effects. In contrast, the tilted conical phase is accompanied by strong dissipation and higher-harmonic contributions, while the transition fields are essentially nonhysteretic. The formation of the second skyrmion phase and tilted conical phase are found to be insensitive to a vanishing demagnetization factor. A quantitative estimate of the temperature dependence of the magnetocrystalline anisotropy may be consistently inferred from the magnetization and the upper critical field and agrees well with a stabilization of the low-temperature skyrmion phase and tilted conical state by conventional cubic magnetic anisotropies.