Would a double deadbolt on a door be more secure than one?

Lately we've been having disturbances and break-in's in our apartment building, so I have been considering upping the security factor of our entry door. I'm not worried about the windows because we are on the 2nd floor and our windows are located in an area that isn't accessible. The door currently has a single cylinder deadbolt and a non-locking door handle on it. I'm only going off of umption here but would a second deadbolt to replace the non locking handle provide more security (i.e. make it much harder to pry the door open? it's not a wooden door, appears to be metallic, the door that is)? I was also thinking of adding a cheap bolt latch (like you see on fence doors and such) on the inside to lock as well while we are home. Would this help more with a second deadbolt or will it not make much of a difference?