Anti-malware software vendors generally do not recommend using multiple active security solution at a time, because they may conflict with each other. Please see this FAQ article.
On the other hand, different security solutions used different virus databases, so if a certain threat slips through one protection layer, it is likely the other will catch it. It is never recommended to have multiple resident protection services enabled though. If you would like to install additional security solution, I recommend disabling it's active components and use it only for on demand scanning (when you suspect the system to be infected).
Maybe AVG users will share their experience here. Some of them do use AVG and Malwarebytes together.
Sorry if this is elementary to some of you. If I have AVG and keep it updated, would additional anti-malware protection be advantageous? (Such as Malware Bytes) I am getting ready to remove the Norton 360 that was preloaded on my new laptop and am a little cautious.