Departing from both sequential pipelines and monotask systems, we propose Multiple Tasks Integration (MTI), a multitask paradigm orthogonal to weight sharing. The essence of MTI is to process the input iteratively but concurrently at multiple levels of analysis, where each decision is based on all of the structures that are already inferred and free from usual ordering constraints. We illustrate MTI with a system that performs part-of-speech tagging, syntactic dependency parsing and semantic dependency parsing. We observe that both the use of reinforcement learning and the release from sequential constraints are beneficial to the quality of the syntactic and semantic parses. We also observe that our model adopts an easy-first strategy that consists, on average, of predicting shorter dependencies before longer ones, but that syntax is not always tackled before semantics.