Recent years witnessed several advances in developing multi-goal conversational recommender systems (MG-CRS) that can proactively attract users' interests and naturally lead user-engaged dialogues with multiple conversational goals and diverse topics. Four tasks are often involved in MG-CRS, including Goal Planning, Topic Prediction, Item Recommendation, and Response Generation. Most existing studies address only some of these tasks. To handle the whole problem of MG-CRS, modularized frameworks are adopted where each task is tackled independently without considering their interdependencies. In this work, we propose a novel Unified MultI-goal conversational recommeNDer system, namely UniMIND. In specific, we unify these four tasks with different formulations into the same sequence-to-sequence (Seq2Seq) paradigm. Prompt-based learning strategies are investigated to endow the unified model with the capability of multi-task learning. Finally, the overall learning and inference procedure consists of three stages, including multi-task learning, prompt-based tuning, and inference. Experimental results on two MG-CRS benchmarks (DuRecDial and TG-ReDial) show that UniMIND achieves state-of-the-art performance on all tasks with a unified model. Extensive analyses and discussions are provided for shedding some new perspectives for MG-CRS.