I assume multi-target refers to a multi-class classification, i.e. each sample corresponds to one target only.
If that’s the case, you could create the last linear layer with out_features=nb_classes, such that each sample will yield the logits for all classes.
For the criterion you could use nn.CrossEntropyLoss, which expects the model output to be raw logits in the shape [batch_size, nb_classes] (which should be the case using the mentioned modification) and a target in the shape [batch_size], containing the class indices in the range [0, nb_classes-1].
If you are working on a regression task, you could also modify the last linear layer and set out_features=regression_features, where regression_features would refer to the number of features your model should predict.
You could add an additional activation function, but it depends on your use case.
nn.MSELoss could be used as the criterion (also nn.L1Loss etc.). The target should have the same shape as the model output in this case.