Maybe could you compute the overlapping between categories pair-wise, then plot the resulting matrix with a heat map for visualization purpose, with plt.matshow ?
With A the numpy array of the one hot labels, of shape (N, d), N the number of examples, d the number of categories, I would do:
common_occurences = A.T@A
This does the cross product of each category with each other, thus every value of the resulting matrix is the count of how often has a category occured with another in the examples.
Then, you can have a global visualization.
import matplotlib.pyplot as plt
plt.matshow(common_occurences)
You might want to normalize your matrix if some categories are overall more present than other in the dataset, because their pair co-occurences will be much higher than others, eventhough they don't happen together more frequently than not.