LHCb has recently reported the first observation of a four-body baryonic B→B1B¯1′B2B¯2′ decay, where B1B¯1′ and B2B¯2′ represent the two pairs of octet baryon states. In our classification, the measured B¯0→pp¯pp¯ decay is a tree dominated process via internal W-boson emission, whose branching fraction is explained as small as 2.2×10−8. We investigate for the first time the phenomenology of other tree and penguin dominated B→B1B¯1′B2B¯2′ decays, and predict the presence of a double threshold effect, manifested as two peaks around mB1B¯1′∼mB1+mB¯1′ and mB2B¯2′∼mB2+mB¯2′ in the invariant mass spectra of B1B¯1′ and B2B¯2′, respectively. Moreover, we predict the following branching fractions: B(B−→np¯pp¯)=(1.7−0.2+0.4±0.1−0.4+0.7)×10−7, B(B−→Λp¯pp¯)=(7.4−0.2+0.6±0.03−2.6+3.6)×10−7, and B(B¯s0→ΛΛ¯pp¯)=(1.9−0.1+0.3±0.01−0.6+1.1)×10−7, which are accessible to experimental facilities.