Ever since the discovery of neutrinos, one question has daunted us, are neutrinos their own antiparticles? One remarkable possibility is that neutrinos have a pseudo-Dirac nature, truly Majorana neutrinos which behave, for all practical purposes, as Dirac fermions, only distinguishable by tiny masssquared differences. Such mass differences would induce oscillations that could only be conspicuous over astrophysical baselines. We analyze the neutrino data from SN1987A in the light of these activesterile oscillations and find a mild preference (∆χ 2 ≈ 3) for a non-zero quadratic mass difference δm 2 = 6.31 × 10 −20 eV 2 . Notably, the same data is able to exclude δm 2 ∼ [2.55, 3.01] × 10 −20 eV 2 with ∆χ 2 > 9, the tiniest mass differences constrained so far. We further consider the future sensitivity of next-generation experiments like the Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande (HK) and demonstrate that, for a future galactic SN occurring at 10 kpc, mass-squared differences as small as ∼ 10 −20 eV 2 could be explored.