This is an option for the function monodromySolve which uses a flower graph. That is, the seed system is the central vertex of the graph; it is connected to all other vertices by two paths, thus creating a "petal" for each additional vertex.

i1 : R = CC[a,b,c,d][x,y]; |

i2 : polys = polySystem {a*x+b*y^2,c*x*y+d}; |

i3 : monodromySolve(polys,GraphInitFunction => flowerGraphInit) o3 = (HomotopyNode{...7...}, 24) o3 : Sequence |

The object flowerGraphInit is a function closure.