Recently, multi-decoder and universal models have attracted increased interest in speech and language processing as they allow learning common representations across tasks. These models learn a common representation by sharing a part of or all network parameters. Moreover, such a universal model can handle tasks unseen during training (zero-shot tasks). However, these models do not fully exploit inter-dependencies between tasks during decoding since they usually perform decoding for each task independently. In this paper, we propose to address this issue by extending the universal model to perform multi-task parallel decoding with a cross-attention module between decoders to capture task inter-dependencies explicitly. We also introduce a novel multi-stream beam search algorithm to allow such parallel decoding. We test our proposed model on multi-lingual (English and Portuguese) text/speech translation and summarization, confirming its potential, especially in zero-shot tasks.