Classification is a fundamental task for metadata estimation in archival document management within a digital library. Although pre-trained language models (PLMs) have evolved significantly, multi-label long text classification (MLLTC) remains challenging for PLM-based text classification methods due to their input text length limitations. Existing PLM-based classifiers typically utilize a single representation for a long text. In contrast, this paper explores a sentence-level classification approach. The basic idea is two-fold: a sentence in a text can often focus on one or a few classes, meaning multiple classes can be derived from the individual sentences; furthermore, sentences can typically fit within the length limit. There are two main issues with implementing a sentence-level classifier: the loss of context for each sentence and the increased training cost due to the larger number of documents that need to be processed by a PLM-based model. To address these issues, this paper proposes a framework, ASC, that uses sentence-level n-grams to form a sentence representation and employs a sentence selection method to reduce the number of sentences needed for training. The experimental results demonstrate that ASC outperforms existing text-level classifiers, achieving 25% and 48% improvements in Macro F1 metrics.