Traditionally, logic synthesis constrains the solution space of later design steps, such as physical design, because they are applied in sequence. Rewiring is a technique to restructure a circuit while maintaining its functionality. Since design properties and objectives can be considered during post-synthesis rewiring, it can help relieve constraints put forth by decisions made at earlier design steps. The extent of rewiring of a rewiring algorithm has a great impact on the success of the design flow. This paper presents a powerful rewiring technique that in addition to unifying all previously proposed Set-of-Pairs-of-Functions-to-be-Distinguished based rewiring techniques, it can perform rewiring with more than one wire which increases our ability to circumvent poorly-decided early design constraints. With this ability, the rewiring ability of using different numbers of wires is reported for the first time in this paper. Our technique can be used for run-time/quality trade-off in any given rewiring application.