In multi-domain task-oriented dialogue systems, users proactively propose a series of domain-specific requests that can often be under-or over-specified, sometimes with ambiguous and cross-domain demands. System-sided initiative would be necessary to identify certain situations and appropriately interact with users to resolve them. However, most existing task-oriented dialogue systems fail to consider such mixed-initiative interaction strategies, performing low efficiency and poor collaboration ability in human-computer conversation. In this paper, we construct a multi-domain task-oriented dialogue dataset with mixed-initiative strategies named TITAN from the large-scale dialogue corpus MultiWOZ 2.1. It contains a total of 1,800 human-human conversations where the system can either ask clarification questions actively or provides relevant information to address failure situations and implicit user requests. We report the results of several baseline models on system response generation and dialogue act prediction to assess the performance of SOTA methods on TITAN. These models can capture mixed-initiative dialogue acts, while remaining the deficiency to actively generate implicit requests and accurately provide alternative information, suggesting ample room for improvement in future studies.