The transiting planet WASP-12 b was identified as a potential target for transit-timing studies because a departure from a linear ephemeris has been reported in the literature. Such deviations could be caused by an additional planet in the system. We attempt to confirm the claimed variations in transit timing and interpret their origin. We organised a multi-site campaign to observe transits by WASP-12 b in three observing seasons, using 0.5-2.6-metre telescopes. We obtained 61 transit light curves, many of them with sub-millimagnitude precision. The simultaneous analysis of the best-quality datasets allowed us to obtain refined system parameters, which agree with values reported in previous studies. The residuals versus a linear ephemeris reveal a possible periodic signal that may be approximated by a sinusoid with an amplitude of 0.00068+/-0.00013d and period of 500+/-20 orbital periods of WASP-12 b. The joint analysis of timing data and published radial velocity measurements results in a two-planet model that explains observations better than do single-planet scenarios. We hypothesise that WASP-12 b might not be the only planet in the system, and there might be the additional 0.1M_Jup_ body on a 3.6-d eccentric orbit. A dynamical analysis indicates that the proposed two-planet system is stable on long timescales.