Multi-task learning for Multi-label classification?
MTL is supposed to enable your shared layer to generalise better.For eg. in a text classification problem your encoder would be trained on separate tasks:
one could be multi class classification(original task) itself and let's take  identifying the sentiment of the sentence(again a classification task; but different than the original task) as the other task.  

For each of these tasks encoder will be same but heads(decoders) will be different.

Decoder/head of one task won't be affected by the other task.

MTL always makes sense. Your encoder/shared layers will be able to generalise better putting less load on your decoders which in turn will increase the performance.