  Let $E/\mathbb{Q}$ be an elliptic curve with ordinary reduction at a prime
$p$, and let $K$ be an imaginary quadratic field. The anticyclotomic Iwasawa
main conjecture, depending upon the sign of the functional equation of
$L(E/K,s)$, predicts the behavior of Selmer group of $E/\mathbb{Q}$ along the
anticyclotomic tower of $K$. Some of the crucial ideas of Bertolini and Darmon
on this conjecture have been abstracted by Howard into an axiomatic set-up
through a notion of Bipartite Euler systems, assuming that $E[p]$ is an
irreducible representation of $G_{K}$. We generalize this work by assuming only
$(E[p])^{G_K}=0$. We use the results of Howard, Nekov\'a\v{r} and Castella
\emph{et al}., along with those of Mazur and Rubin on Kolyvagin systems to show
one divisibility of the anticyclotomic main conjecture, for both the signs. The
other divisibility can be reduced to proving the nonvanishing of sufficiently
many $p$-adic $L$-functions attached to a family of congruent modular forms.
