T2K (Tokai to Kamioka), the world's first off-axis long-baseline neutrino beam experiment, was built for the precision measurement of neutrino oscillations. T2K makes use of a highly intense and almost pure $\nu_{\mu}$/$\overline{\nu}_{\mu}$ beam produced at the J-PARC accelerator complex and sent 295 km across Japan to the far detector, Super-Kamiokande. After the $\nu_{\mu}\rightarrow \nu_e$ appearance was observed at T2K in 2013, confirming the non-zero mixing angle $\theta_{13}$, T2K started to search for the first time for experimental evidence of CP violation in neutrino oscillations. To enhance this search substantially, the T2K collaboration is proposing an extension of data taking until 2026 for an overall accumulation of $20\times10^{21}$ protons-on-target (POT). This amount of data, along with T2K hardware upgrades and analysis improvements, allows us to intensively explore CP violation in the lepton sector, to precisely measure neutrino oscillation parameters, and to positively search for unknown physics.