We report x-ray photon correlation spectroscopy experiments on the dynamics of the glass-former polypropylene glycol covering a temperature range from room temperature to the glass transition at T g = 205 K using silica tracer particles. Three temperature regimes are identified: At high temperatures, Brownian motion of the tracer particles is observed. Near T g , the dynamics is hyperdiffusive and ballistic. Around 1.12T g , we observe an intermediate regime. Here the stretching exponent of the Kohlrausch-Williams-Watts function becomes q dependent. By analyzing higher-order correlations in the scattering data, we find that dynamical heterogeneities dramatically increase in this intermediate-temperature regime. This leads to two effects: increasing heterogeneous dynamics and correlated motion at temperatures close to and below 1.12T g .