We study the full angular distribution of semileptonic rare charm baryon decays in which the secondary baryon undergoes weak decay with sizable polarization parameter, $$\Xi _c^+\rightarrow \Sigma ^+\,(\rightarrow p\pi ^0)\ell ^+\ell ^-$$ ${\Xi }_c^{+}\to {\Sigma }^{+}(\to p{\pi }^0){\ell }^{+}{\ell }^{-}$ , $$\Xi _c^0\rightarrow \Lambda ^0\,(\rightarrow p \pi ^-)\ell ^+\ell ^-$$ ${\Xi }_c^0\to {\Lambda }^0(\to p{\pi }^{-}){\ell }^{+}{\ell }^{-}$ and $$\Omega _c^0\rightarrow \Xi ^0\,(\rightarrow \Lambda ^{0} \pi ^0)\ell ^+\ell ^-$$ ${\Omega }_c^0\to {\Xi }^0(\to {\Lambda }^0{\pi }^0){\ell }^{+}{\ell }^{-}$ . Such self-analyzing decay chains allow for seven additional observables compared to three-body decays such as $$\Lambda _c \rightarrow p \ell ^+ \ell ^-$$ ${\Lambda }_c\to p{\ell }^{+}{\ell }^{-}$ , with different sensitivities to the $$|\Delta c|=|\Delta u|=1$$ $\left|\Delta c\right|=\left|\Delta u\right|=1$ weak couplings. Opportunities to test the standard model in $$c \rightarrow u$$ $c\to u$ transitions with standard model null tests and other angular observables are worked out. We show that a joint model-independent analysis of the leptonic $$A_{\text {FB}}^\ell $$ $A_{\text{FB}}^{\ell }$ , hadronic $$A_{\text {FB}}^{\text {H}}$$ $A_{\text{FB}}^{\text{H}}$ , and combined forward–backward asymmetry $$A_{\text {FB}}^{\ell \text {H}}$$ $A_{\text{FB}}^{\ell \text{H}}$ together with the fraction of longitudinally produced leptons, $$F_L$$ $F_L$ , is able to pin down the dipole couplings $$C_{7},C^\prime _{7}$$ $C_7,C_7^{\prime }$ and the semileptonic (axial-) vector ones $$C_{10},C^\prime _{9},C^\prime _{10}$$ $C_{10},C_9^{\prime },C_{10}^{\prime }$ . $$A_{\text {FB}}^{\text {H}}$$ $A_{\text{FB}}^{\text{H}}$ is also accessible with dineutrino $$c \rightarrow u \nu {\bar{\nu }}$$ $c\to u\nu \overline{\nu }$ modes and probes right-handed currents.