Twinning is a key deformation mechanism in face-centered-cubic (fcc)-based and some body-centered-cubic (bcc)-based alloys, which imparts excellent strength-ductility combination by increasing strain-hardenability. Typically, twinning in fcc-based alloys increases when the stacking fault energy is lowered via changes in composition. The present study clearly demonstrates that deformation twinning can be enhanced when hard-intermetallic compounds like ordered B2 and sigma phases form in the fcc matrix of a high entropy alloy (HEA), leading to an excellent combination of strength, ductility, and strain-hardenability. Such a combination of properties was achieved by exploiting the novel and often unusual phase stability regimes that can be accessed in these complex concentrated HEAs. The present study exploits a unique three-phase mixture of recrystallized fine-grained fcc + B2 + sigma in a prototypical Al0.3CoCrFeNi HEA to demonstrate this effect. Coupling transmission electron microscopy and molecular dynamics simulations revealed that B2 grains enhance deformation twinning by raising the local stress levels, consequently forming substantially thicker twins as compared to the single fcc-phase condition of Al0.3CoCrFeNi. The local stresses were further accommodated via nano-twinning, limited B2 plasticity, and highly restricted micro-cracks in and around the sigma grains.