Most word embeddings today are trained by optimizing a language modeling goal of scoring words in their context, modeled as a multiclass classification problem. Despite the successes of this assumption, it is incomplete: in addition to its context, orthographical or morphological aspects of words can offer clues about their meaning. In this paper, we define a new modeling framework for training word embeddings that captures this intuition. Our framework is based on the well-studied problem of multi-label classification and, consequently, exposes several design choices for featurizing words and contexts, loss functions for training and score normalization. Indeed, standard models such as CBOW and FAST-TEXT are specific choices along each of these axes. We show via experiments that by combining feature engineering with embedding learning, our method can outperform CBOW using only 10% of the training data in both the standard word embedding evaluations and also text classification experiments.