As a beginner, it's best to just keep adding weight to the bar, and if you feel a burning desire to add volume, do it after your heavy sets for the day. IMO it's something you'd do for hypertrophy, but as stated previously, it's one of those controversial things.
That said, I see a LOT of people doing high volume who shouldn't be - the guys who I used to train with went on to do 10x10 for some reason and naturally went backwards in terms of weight on the bar. Who trains to get weaker?!
For me, upping the intensity can be doing more reps in a set (for assistance as it's a variable), or just taking less rest time between sets. I also agree that the single most important part of any program, no matter what it is, is effort. Again, I see a positive correlation between the amount of visible effort someone puts in to results gained.