Classification of data streams has gained a lot of popularity in recent years owing to its multiple applications. In certain applications like community detection from text feeds, website fingerprinting attack, etc., it is more meaningful to associate class labels with groups of objects rather than the individual objects. This kind of classification problem is known as the set-wise classification problem. The few algorithms available in literature for this problem are budget algorithms, i.e. they are designed to process fixed maximum stream speed, and are not capable of handling variable and high speed streams. We present ANYSC which is the first anytime set-wise classification algorithm for data streams. ANYSC handles variable inter-arrival rate of objects in the stream and performs classification of test entities within any available time allowance, using a proposed data structure referred to as CProf-forest. The experimental results show that ANYSC brings in the features of an anytime algorithm and outperforms the existing approaches.