What's a classifier capable of predicting a variable number of classes I want to solve what I understand as a classification problem regarding tagging. Let's say an Entity can have 0 or more tags and I want to be able to predict which tags (if any) an entity might get

I would like the classifier to output 0 or more tags.

I have never run into this kind of structure with variable length in input data (many tags) and output (0, one or more tags for each entity) before and I'm not even sure what terminology / words to search for.
This is an interesting problem. What is your xtrain? I guess it boils down to a multi label problem. In a simple setup, you would train on the presence of a certain label (present or not). So for n tags/labels, you would train n+1 (1 is no label) models. 

I‘m not really in to multilabel problems, but I guess this is the way to go.