Aims: 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. Methods: We organised a multi-site campaign to observe transits by WASP-12 b in three observing seasons, using 0.5-2.6-metre telescopes. Results: 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 ± 0.00013 d 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 0.1 MJup body on a 3.6-d eccentric orbit. A dynamical analysis indicates that the proposed two-planet system is stable on long timescales. Partly based on (1) data collected with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, (2) observations made at the Centro Astronómico Hispano Alemán (CAHA), operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC), (3) data collected with telescopes at the Rozhen National Astronomical Observatory, and (4) observations obtained with telescopes of the University Observatory Jena, which is operated by the Astrophysical Institute of the Friedrich-Schiller-University.Tables 2 and 3 are available in electronic form at http://www.aanda.orgLight curves are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/551/A108