Double Supersolid Phase in a Bosonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mtext>−</mml:mtext> <mml:mi>J</mml:mi> <mml:mtext>−</mml:mtext> <mml:mi>V</mml:mi> </mml:mrow> </mml:ma

Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this Letter, we investigate a bosonic t-J-V model currently realized with Rydberg atoms. Through large-scale quantum Monte Carlo simulations, we uncover an emergent double supersolid (DSS) phase with the coexistence of two superfluids and crystalline order. Tunable long-range tunneling and repulsive hole-hole interactions enable a rich phase diagram featuring a double superfluid phase, a DSS phase, and an antiferromagnetic insulator. Intriguingly, within the DSS regime we observe an unconventional thermal enhancement of crystalline order. Our results establish the bosonic t-J-V model as a promising and experimentally accessible platform for exploring exotic quantum phases in Rydberg atom arrays.