Opinion summarization is the task of automatically generating summaries for a set of opinions about a specific target (e.g., a movie or a product). Since the number of input documents can be prohibitively large, neural network-based methods sacrifice end-to-end elegance and follow a two-stage approach where an extractive model first pre-selects a subset of salient opinions and an abstractive model creates the summary while conditioning on the extracted subset. However, the extractive stage leads to information loss and inflexible generation capability. In this paper we propose a summarization framework that eliminates the need to pre-select salient content. We view opinion summarization as an instance of multi-source transduction, and make use of all input documents by condensing them into multiple dense vectors which serve as input to an abstractive model. Beyond producing more informative summaries, we demonstrate that our approach allows to take user preferences into account based on a simple zero-shot customization technique. Experimental results show that our model improves the state of the art on the Rotten Tomatoes dataset by a wide margin and generates customized summaries effectively.