Searches for new phenomena inspired by supersymmetry in final states containing an $e^+e^-$ or $\mu ^+\mu ^-$ pair, jets, and missing transverse momentum are presented. These searches make use of proton–proton collision data with an integrated luminosity of $139~\text {fb}^{-1}$, collected during 2015–2018 at a centre-of-mass energy $\sqrt{s}=13~$TeV by the ATLAS detector at the Large Hadron Collider. Two searches target the pair production of charginos and neutralinos. One uses the recursive-jigsaw reconstruction technique to follow up on excesses observed in $36.1~\text {fb}^{-1}$ of data, and the other uses conventional event variables. The third search targets pair production of coloured supersymmetric particles (squarks or gluinos) decaying through the next-to-lightest neutralino $(\tilde{\chi }_2^0)$ via a slepton $(\tilde{\ell })$ or Z boson into $\ell ^+\ell ^-\tilde{\chi }_1^0$, resulting in a kinematic endpoint or peak in the dilepton invariant mass spectrum. The data are found to be consistent with the Standard Model expectations. Results are interpreted using simplified models and exclude masses up to 900 GeV for electroweakinos, 1550 GeV for squarks, and 2250 GeV for gluinos.