We discuss the status of resummation of large logarithmic contributions to groomed event shapes of hadronic final states in electron-positron annihilation. We identify the missing ingredients needed for next-to-next-to-next-to-leading logarithmic (NNNLL) resummation of the modified mass mass drop tagger (mMDT) groomed jet mass in $e^{+}{e}^{-}$ collisions: the low-scale collinear-soft constants at two-loop accuracy, $c_{S_c}^{\left(2\right)}$, and the three-loop noncusp anomalous dimension of the global soft function, ${\gamma }_S^{\left(2\right)}$. We present a method for extracting those constants using fixed-order codes: the event2 program to obtain the color coefficients of $c_{S_c}^{\left(2\right)}$, and mccsm for extracting ${\gamma }_S^{\left(2\right)}$. We present all necessary formulae for resummation of the mMDT groomed heavy jet mass distribution at NNNLL accuracy.