Chord detection is the task of assigning chord labels to segments of an input musical piece. The labels are typically drawn from a pre-defined vocabulary in which each symbol comprises at least a root pitch and a chord quality. In this paper, we introduce a post-processing method that takes as input a musical score with such labels and adds chord tone alterations such as suspensions to them. Although it is an important aspect of harmonic analysis, it is infeasible to do so by simply adding features to the labels in the vocabulary, given the multiplicative effect on vocabulary sizes which can already be over 1000. We evaluate our method using both ground truth input and input derived from a chord detection model, showing that it outperforms a strong heuristic baseline in both cases. Furthermore, we show that our model can be used to detect the rarer chord qualities from the model's output alterations, potentially enabling chord detection models to be trained on small vocabularies containing only the more common (and easier to identify) chord qualities (e.g. only triads).