Can I use the training rows multiple times while training with different labels attached to it?
The problem you are describing is a perfect use case for Fuzzy Logic.

Contrary to boolean logic where things are either black or white, fuzzy logic allows things to be grey.

Take the example of weather. Given a temperature, some people might say it is cold whereas other would say it is warm. There will be situations where all say it is cold, but there exists a mid-term where the classification isn't $\{0,1\}$ but rather $[0,1]$.



Therefore, it won't be a problem given that your chosen algorithm allows for probabilistic output.

So given the temperature example. You have the classes [cold, warm, hot].
If your algorithm can only output binary classifications (e.g. [0, 1, 0]), then better only input data points with only 1 label. However, if your algorithm can output probabilistic classifications (e.g. [0.2, 0.7, 0.1]) then you can input the same datapoint with multiple labels.

In the end, you can pick the class with the largest probability, but you need to understand that this might not give the output you are expecting. If you get a classification of [0.49, 0.51, 0.0], you might say is class 2 where in truth the model is not actually telling you that.