Context. Afterglows of gamma-ray bursts (GRBs) are simple in the most basic model, but can show many complex features. The ultra-long duration GRB 111209A, one of the longest GRBs ever detected, also has the best-monitored afterglow in this rare class of GRBs. Aims. We want to address the question whether GRB 111209A was a special event beyond its extreme duration alone, and whether it is a classical GRB or another kind of high-energy transient. The afterglow may yield significant clues. Methods. We present afterglow photometry obtained in seven bands with the GROND imager as well as in further seven bands with the Ultraviolet/Optical Telescope (UVOT) on-board the Neil Gehrels Swift Observatory. The light curve is analysed by multi-band modelling and joint fitting with power-laws and broken power-laws, and we use the contemporaneous GROND data to study the evolution of the spectral energy distribution. We compare the optical afterglow to a large ensemble we have analysed in earlier works, and especially to that of another ultra-long event, GRB 130925A. We furthermore undertake a photometric study of the host galaxy. Results. We find a strong, chromatic rebrightening event at ≈0.8 days after the GRB, during which the spectral slope becomes redder. After this, the light curve decays achromatically, with evidence for a break at about 9 days after the trigger. The afterglow luminosity is found to not be exceptional. We find that a double-jet model is able to explain the chromatic rebrightening. The afterglow features have been detected in other events and are not unique. Conclusions. The duration aside, the GRB prompt emission and afterglow parameters of GRB 111209A are in agreement with the known distributions for these parameters. While the central engine of this event may differ from that of classical GRBs, there are multiple lines of evidence pointing to GRB 111209A resulting from the core-collapse of a massive star with a stripped envelope.