Ossification of the Internet transport-layer architecture is a significant barrier to innovation of the Internet. Such innovation is desirable for many reasons. Current applications often need to implement their own mechanisms to receive the transport service they need, but many do not have the breadth of adapting to all possible network characteristics. An updated transport architecture can do much to make the Internet more flexible and extensible. New ground-breaking services often require different or updated transport protocols, could benefit from better signalling between application and network, or desire a more flexible choice of which network path is used for which traffic. This document therefore proposes a new transport architecture. Such architecture lowers the barrier to service innovation by proposing a “transport system”, the NEAT System, that can leverage the rich set of available transport protocols. It paves the way for an architectural change of the Internet where new transport-layer services can seamlessly be integrated and quickly made available, minimising deployment difficulties, and allowing Internet innovators to take advantage of them wherever possible. The document provides a survey of the state-of-the-art to identify the architectural obstacles to, and opportunities for, evolution of the transport layer. It also details a set of general requirements for a new transport architecture. This new architecture is motivated by a set of use-cases, followed by a description of the NEAT architecture for a transport system, designed to permit applications to select appropriate transports based on their needs and the available transport services.