Sure you can, but you're going to need a way of varying your program over time. It could be as simple as increasing the volume, but I don't think that's going to be super effective. You may have to add weight eventually.
Another thing is that you may be lacking in hamstring and glute development, so things like reverse hyperextensions and glute ham raises would be good additions.
You CAN but its not the most efficient or effective way of doing it. At some point the amount of work you will need to do to stimulate new growth will be almost totally cancelled out by how much energy you'll expend getting to that point. You'll simply get too strong for your bodyweight to provide enough resistence.
That said, if you're a beginner a few months of bodyweight only training will only mean good things when you finally do get to workout with some weights. They're a fantastic way of building a good base.
The number of people who i see on the bench press who can barely do a few bodyweight pushups is staggering. Similar situation with pullups and lat pulldowns.
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