The accelerator-based measurement of the leptonic Dirac CP phase $\delta_D$ in neutrino mixing suffers from multiple intrinsic shortcomings. Even within the paradigm of three-neutrino oscillation with only the standard interactions predicted by the Standard Model (SM), accelerator neutrino experiments have several issues: 1) low efficiency and event rates, 2) $\delta_D$ vs $\pi - \delta_D$ degeneracy, and 3) large uncertainty for maximal CP, $\delta_D \sim \pm \frac \pi 2$ which is unfortunately or fortunately preferred by recent global fit. Going beyond the SM, new physics alternatives such as: 4) non-unitary mixing (NUM) and 5) non-standard interactions (NSI) can fake the CP violation effect and hence significantly reduce the sensitivity of the
genuine Dirac CP phase. Especially, there is not just 5a) vector type NSI, but also 5b) scalar and 5c) dark NSI that can correct and fake the neutrino mass term in the effective Hamiltonian. The current and future accelerator-based experiments (such as T2K/T2K-II/T2HK/T2HKK, NO$\nu$A, and DUNE) can probably gather firm data, interpreting the Dirac CP phase out of it is significantly subject to theoretical assumptions. Unless extra experimental configuration is specifically designed to test these theoretical alternatives,
no conclusive result can be reached. The TNT2K configuration, a combination of T2K/T2HK running purely on the neutrino mode and $\mu$SK/$\mu$HK (muon decay at rest source plus the SK/HK detector) focusing on the antineutrino mode, can solve the aforementioned issues from item 1) to item 5a). For 5b) and 5c), synergy of even more types of neutrino experiments.