This work examines the scenario of ATR classification in multi-label settings by using the framework of a classification sequence. Classification tasks are often composed of a sequence of identification tasks that together, generate an overall classification. For instance, objects may be sorted and classified as one particular target type and then those targets are further identified. Rather than passing all objects through each classifier, a sequence of classifiers may be used to identify objects without the need to process data through each classifier. Such sequences exist for two-label outcomes (such as target and non-target) and have been called: Believe the Negative, Believe the Positive, and Believe the Extremes. In each of these sequences, the first classification system is able to identify objects such that only a portion of objects must be passed to the second system for identification. However, to extend these sequences to k-labels, a new definition of the ordering on the labels must be generated in order to incorporate all k-labels into the classification sequence. In this work, we develop the mathematical structures that exist for a k-label classification sequence, provides formula for both the optimal performance and operational cost of these sequences, and examines the performance of such sequences under a variety of operating conditions. Conceptually, we will begin and demonstrate these results with a 3-label ATR system. In conclusion, this work will demonstrate the utility of using a sequence to fuse information in a multi-label classification task.