Add a symbol to an existing library

I created a symbol library and I would like to add additional symbols to it. I have tried dragging the paths from the artboard to the new library but it won't let me add it. I can't seem to transfer it from the default symbol library to the new library tab either. The only thing I can do is to overwrite the new library by selecting the symbols in the default library but this seems like the wrong way to go about it.

Hope you can help.