Plan recognition is a ubiquitous task in the artificial intelligence and pervasive computing research. Multiple-goal recognition problem is a major challenge in the real-world of plan recognition, in which users often pursue several goals in a concurrent and interleaving manner, where the pursuit of goals may spread over different parts of an activity sequence and may be pursued in parallel. Existing approaches to recognizing multiple-goal problems are probabilistic approaches assuming the existence of plan libraries, which require much human effort in predicting and formalizing plans, and may be unrealistic in many cases. In this paper, we present a novel logic-based approach to solve the multiple-goal problems efficiently, without the need of plan libraries, using a state-of-the-art heuristic search planner LAMA. In particular, we propose the first formulation of multiple-goal recognition problem based on planning, and present a two-level probabilistic plan recognition approach that deals with both concurrent and interleaving goals from observed activity sequences. Experimental results over several domains show that our method can recognize multiple-goal problem with flexibility and scalability.