Connector colouring provided an intuitive semantics of Reo connectors which lead to effective implementation techniques, first based on computing colouring tables directly, and later on encodings of colouring into constraints. One weakness of the framework is that it operates globally, giving a colouring to all primitives of the connector in lock-step, including those not involved in the interaction. This global approach limits both scalability and the available concurrency. This paper addresses these problems by introducing partiality into the connector colouring model. Partial colourings allow parts of a connector to operate independently and in isolation, increasing scalability and concurrency.