I hope by now I have convinced you that calisthenics training can be a powerful tool for improving your body composition and increasing muscle mass.
First, let's talk about building muscle. There is something commonly missing in most conversations regarding muscle building. When we talk about building muscle, or putting on size, or training for hypertrophy, the real question is "relative to what?". Walking can elicit significant hypertrophy- under certain scenarios of course, like if your leg had been in a cast for 12 weeks. Working up to 5 sets of 20 push ups can definitely stimulate muscle growth in untrained people, but probably won't stimulate any growth if you already bench 1.5x your bodyweight for a set of 10. There are degrees of hypertrophy. Keep this in mind.
Unlike barbell training, pure calisthenics lack the convenience of just adding weight as you get stronger. Yes, you can add weight to pull ups and squats, but I'm talking about keeping the exercises unweighted. The ability to add weight to a barbell is one reason why it is one of the most effective tools for gaining size. The incremental increase in the training load allows for a useful, easy, convenient and effective progression, and progression builds muscle. Limited to only your bodyweight, this beautifully simplistic method of progression is unavailable. Don't worry though, there are two ways of working around this limitation- adding volume and changing leverage.
Adding volume will stimulate muscle growth, provided a threshold for intensity has been crossed. What exactly that threshold is will vary from person to person, based on genetics and training status (remember the bit about walking and having your leg in a cast). What we do know is that loads as light as a 35 rep max can stimulate just as much hypertrophy as loads in the 8-12 rep range, provided sets are taken to failure (1). We don't know if failure is necessary, but we do know it works. We also don't know if loads lighter than 35 rep max can stimulate hypertrophy to the same degree, but it is reasonable to conclude they would as long as muscular failure is reached.
I built my back with high volume pull ups
Anecdotally, there are enough stories of people gaining mass without going to failure that it is hard to believe that failure, even with lighter loads is required for growth. Aerobic exercise has been shown to significantly increase muscle mass. Running is a far cry from a 35 rep max, and contrary to popular belief, even running has been shown to induce significant hypertrophy (2). Cycling, also considered an aerobic activity, is well documented to increase hypertrophy (3,4). Many people grow from just increasing submaximal volume. Taking your weekly push up volume from 50 to 1500 reps and weekly pull up volume from 25 to 750 reps over a year and you would most likely add some significant muscle mass, whether you went to failure or not. There is something potent about increasing training volume in this manner. Prisoners do this, soldiers do this, and I've seen many people pick up cycling only to be shocked that a few months later their quad growth forced them to buy new pants.
This isn't the only way to grow, and some people hate volume work. If you like to keep your reps low, then changing the leverage can make an exercise harder, increase mechanical tension, and stimulate new growth. By continuously moving to harder variations of an exercise as you get stronger, you can keep your rep range wherever you want. Assuming you start from scratch, you might begin your push up training with 3 sets of 4-8 push ups. Once you are competently performing all of your sets at the upper end of your rep range, you might move to diamond push ups for 3 sets of 4-8. Fill out the rep range and move to feet elevated diamond push ups. Repeat this process through archer push ups, feet elevated archer push ups, 1 arm push ups, and feet elevated 1 arm push ups. This process will build strength and muscle very effectively as you manipulate leverage and bodyweight to increase mechanical tension on the target muscle.
Both of these methods work. Metabolic stress, mechanical tension and muscle damage all are capable of stimulating growth. If maximizing the hypertrophic response is your top priority, then it would be best to use both of these methods. Start your training session with a movement that you plan on progressing through harder and harder variations of over time. Follow this up with movements that you work on adding volume to. A snapshot of a single session might look like this:
Archer Pull Up (1 Arm Pull Up Progression) 4 sets of 4
Feet Elevated Archer Push Up (1 Arm Push Up Progression) 4 sets of 6
Diamond Push Ups 5 Sets of 45
Chin Ups 5 sets of 16
While hypertrophy responses are likely to be the same between these two methods, the performance adaptations will certainly not be. Both methods will increase strength and endurance, but they will do so in dramatically different proportions. By progressing through harder and harder variations of a movement, you increase the mechanical stress on a muscle and make it significantly stronger. Yes, you will get a little better conditioned, but your primary adaptation will be strength. By exposing a muscle to more volume and higher levels of metabolic stress, the muscle will adapt to the training by better tolerating metabolic stress and greatly increasing its resistance to fatigue. Essentially, hypertrophy happens regardless.
So pick whichever method suits you the most. Better yet, vary it so your muscles get a wide variety of intensities and volume.