Sentiment analysis refers to the automatic collection, aggregation, and classification of data collected online into different emotion classes. While most of the work related to sentiment analysis of texts focuses on the binary and ternary classification of these data, the task of multi-class classification has received less attention. Multi-class classification has always been a challenging task given the complexity of natural languages and the difficulty of understanding and mathematically "quantifying" how humans express their feelings. In this paper, we study the task of multi-class classification of online posts of Twitter users, and show how far it is possible to go with the classification, and the limitations and difficulties of this task. The proposed approach of multi-class classification achieves an accuracy of 60.2% for 7 different sentiment classes which, compared to an accuracy of 81.3% for binary classification, emphasizes the effect of having multiple classes on the classification performance. Nonetheless, we propose a novel model to represent the different sentiments and show how this model helps to understand how sentiments are related. The model is then used to analyze the challenges that multi-class classification presents and to highlight possible future enhancements to multi-class classification accuracy.