Doing more is the common misconception people have for bringing up weak body parts. This is exactly what you should not do. Remember, more is not better with respect to volume. When people take this approach, they end up quickly over-training their lagging muscle groups and thus further suppressing gains in muscle size and strength.
The answer here is “intensity, focus, and overload.” You want to train with maximum intensity, maximum mental focus, and maximum overload.
To optimize these areas for lagging muscle groups, you should structure your workout where you train these areas first, at the beginning of each training rotation. For example, let’s say your back is your weak body part. This muscle group should be trained first. If you train Monday through Friday, your back workout should be performed on Monday.
Also, make sure you start your workout with a major compound movement. In this case, bent over barbell rows or low-pull cable rows will take advantage of maximum overload for your back.
By training your lagging muscle groups first, at the beginning of each training rotation and the beginning of each workout, this will allow you to train these muscle groups with the highest intensity and mental focus so you can maximize the overload used for the greatest amount of muscle fiber stimulation.