If you want to add strength, then you must change the exertion your body (muscles) has become used to over the past several weeks/months. This is called progressive weight resistance. We need to continuously add stress to the muscles in order for them to grow in size (density) and thus increase strength.
I would not recommend you simply add more sets. After a period, you are not adding greater stress that will have much impact on your muscles besides strengthening tendons and ligaments, both of which are very important. Instead, if you are at the usual 3 sets per muscle group, increase the poundages so that you are being taxed around the 6th rep and on the 9th to 10th rep, you are at the point (if you have a spotter) of total exhaustion.
The above will depend on how you are integrating your initial ‘3 sets’ per muscle group. If the 1st set is a warm up set, then go ahead and add a 4th set. If all 3 sets are incrementally strenuous, then add more weight when 10 reps becomes easy (relatively speaking) to achieve.
Our body will match or adapt to the resistance placed on it. This is why it is important to vary the type of exercises done, the frequency, and fundamentally, the poundages used. This also depends on why you started lifting in the first place.
Be forewarned that moving real heavy weight isn’t necessary for the avg body builder. And that most people are presently using too heavy a weight to achieve maximum range of motion and thus are getting only 60% results from 100% effort. Train hard but smart.
Robin, if you want to achive a specific goal, then ensure your routine involves that specific task. Pullups/chinups for example, are you incorporating pullups as part of your routine? If not, do so within 6-8 weeks of starting your workouts. It will be easier to have a spotter grab your hips (don’t grab the legs as it then becomes too easy to push off with your legs) and assist you by lifting half of your body weight. You can also do half-ups, which are great for the shoulder girdle area. Get a stool or chair, grip the bar and hang, then concentrate on lifting your body with just your upper back- again, visualise the movement. Then let yourself go. Repeat and do them at a moderate pace for 2 sets of 10. I do these to actually increase my shoulder motion and strength. These are also a precursor to pullups (which I use a wrist wrap for).
Hope that helps. As with almost all of my posts, this is exactly how I do thangs.
nospam.