In this study, we focus on a method of searching for similar trajectories. In most previous works on searching for similar trajectories, only raw trajectory data have been used. However, to obtain deeper insights, additional time-dependent trajectory features should be utilized depending on the search intent. For instance, to identify soccer players who have similar dribbling patterns, such additional features include the correlations between players' speeds and directions. In addition, when finding similar combination plays, the additional features include the team players' movements. In this paper, we develop a framework to flexibly search for similar trajectories associated with time-dependent features, called enriched trajectories. In this framework, weights, which represent the relative importance of each feature, can be flexibly input. Moreover, to facilitate fast searching, we propose a lower bounding measure of the DTW distance between enriched trajectories. We evaluate the effectiveness of the lower bounding measure using soccer data and synthetic data. Our experimental results suggest that the proposed lower bounding measure is superior to the existing measure and works very well.