Ant colony optimisation (ACO) for classification has mostly been limited to rulebased approaches where artificial ants walk on datasets in order to extract rules from the trends in the data, and hybrid approaches which attempt to boost the performance of existing classifiers through guided feature reductions or parameter optimisations. A recent notable example that is distinct from the mainstream approaches is PolyACO, which is a proof-ofconcept polygon-based classifier that resorts to ACO as a technique to create multi-edged polygons as class separators. Despite possessing some promise, PolyACO has some significant limitations, most notably, the fact of supporting classification of only two classes, including two features per class. This paper introduces PolyACO+, which is an extension of PolyACO in three significant ways: (1) PolyACO+ supports classifying multiple classes, (2) PolyACO+ supports polygons in multiple dimensions enabling classification with more than two features, and (3) PolyACO+ substantially reduces the training time compared to Poly-ACO by using the concept of multi-levelling. This paper empirically demonstrates that these updates improve the algorithm to such a degree that it becomes comparable to state-of-the-art techniques such as SVM, neural networks, and AntMiner+.