We extend the weighted Nitsche's method proposed in the first part of this study to include multiple intersecting embedded interfaces. These intersections arise either inside a computational domain - where two internal interfaces intersect; or on the boundary of the computational domain - where an internal interface intersects with the external boundary. We propose a variational treatment of both the interfacial kinematics and the external Dirichlet constraints within Nitsche's framework. We modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the Nitsche variational form in the presence of junctions. Finally, we demonstrate the performance of the method for both perfectly-tied interfaces and perfectly-plastic sliding interfaces through several benchmark examples. © 2013 Elsevier B.V.