Because it's a hidden skill, you can only see them getting better by advancing in their career. For that reason, I don't think you could train them in all three, because you have to be employed as a magician to actually do magician things, same for acrobat and singer, although a Sim can sing at the karaoke bar, so that might help.
Also, do you have just one person in the household? because if there is only one Sim in a household, you can't send them on tour to somebody else's game because there will be nobody to mind the house while they are gone.