Middleboxes, such as firewalls, NATs, proxies, and application accelerators are known for their undesirable implications on traffic (mainly due to packet headers or payload modifications) and for hindering connection establishment when certain protocols are in use (e.g., UDP, SCTP).Since many of these implications occur in middleboxes within ISPs or cellular networks, we present a software-defined network (SDN) architecture that can foster the collaboration between end-hosts and ISPs. In particular, an end-host can express a desirable behavior from the network, specified as an invariant (e.g., no IP header or payload modification), and the ISP, in turn, can establish a connection through middleboxes that preserve this invariant. We discuss the proposed architecture and the requirements for invariant preserving middlebox traversal. We further propose an algorithm for the selection of the best path through a sequence of invariant-preserving middleboxes. We use simulations to assess the efficiency of our approach.