We will describe a new strategy to prove the plus-minus main conjecture for elliptic curves having good supersingular reduction at p. It makes use of an ongoing work of Kings-Loeffler-Zerbes on explicit reciprocity laws for Beilinson-Flach elements to reduce to another main conjecture of Greenberg type, which can in turn be proved using Eisenstein congruences on the unitary group U(3,1).