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Network slicing will permit offering to vertical customers tailored end-to-end logical networks in an on-demand fashion, on top of a common telecom infrastructure, achieving a Slices-as-a-Service (SlaaS) business model. This is possible due to the progressive introduction of network softwarization techniques, such as programmability and virtualization, into existing operational networks, enabling dynamic and flexible provision of slices. Those vertical customers could require the control not only of the network functions composing the end-to-end service, but also of the connectivity among them, e.g., for influencing the paths for steering traffic among function instances. However, this can be problematic since decisions from one vertical customer can collide with decisions from others. One aspect not yet sufficiently investigated is how to permit vertical customers to jointly control the service functions and the underlay connectivity, in such a way that could operate the allocated slice as if it was actually a dedicated network entirely for them. This paper explores some architectural proposition in this respect illustrated with some potential use cases and it provides an example of the provision of SlaaS for a vertical customer.