A background of nanohertz gravitational waves from supermassive black hole binaries could soon be detected by pulsar timing arrays, which measure the times-of-arrival of radio pulses from millisecond pulsars with very high precision. The European Pulsar Timing Array uses five large European radio telescopes to monitor high-precision millisecond pulsars, imposing in this way strong constraints on a gravitational wave background. To achieve the necessary precision needed to detect gravitational waves, the Large European Array for Pulsars (LEAP) performs simultaneous observations of pulsars with all five telescopes, which allows us to coherently add the radio pulses, maximize the signal-to-noise of pulsar signals and increase the precision of times-of-arrival. We report on the progress made and results obtained by the LEAP collaboration, and in particular on the addition of the Sardinia Radio Telescope to the LEAP observations during its scientific validation phase. In addition, we discuss how LEAP can be used to monitor strong-gravity systems such as double neutron star systems and impose strong constraints on post-keplerian parameters.