The task of video-to-speech aims to translate silent video of lip movement to its corresponding audio signal. Previous approaches to this task are generally limited to the case of a single speaker, but a method that accounts for multiple speakers is desirable as it allows to i) leverage datasets with multiple speakers or few samples per speaker; and ii) control speaker identity at inference time. In this paper, we introduce a new video-to-speech architecture and explore ways of extending it to the multi-speaker scenario: we augment the network with an additional speaker-related input, through which we feed either a discrete identity or a speaker embedding. Interestingly, we observe that the visual encoder of the network is capable of learning the speaker identity from the lip region of the face alone. To better disentangle the two inputs -- linguistic content and speaker identity -- we add adversarial losses that dispel the identity from the video embeddings. To the best of our knowledge, the proposed method is the first to provide important functionalities such as i) control of the target voice and ii) speech synthesis for unseen identities over the state-of-the-art, while still maintaining the intelligibility of the spoken output.