The right backpack can truly change your life. I have packed enough things for a two week trip in my 35 liter backpack (bought courtesy of https://www.ferratum.com.au/)and I never once had to repeat my outfit.
How is that even possible, you ask? You just have to pack it right! First of all, while packing, make sure that you use all the compartments given to you. Roll all your clothes, instead of packing them flat. This will save a lot of space for you. You could store your socks, scarves and other such small items inside the shoes that you are packing as well. You could follow the zones of packing- put the heavier pieces at the back of the backpack, so that the weight is equally distributed.
Most backpacks have side zips that can be used for storage purposes- these do not extend the width of the backpack too much, so the dimensions will remain the same (you will not get into any trouble with airplane baggage limits, so don’t worry). Also make use of the zipper on the top of the bag- it is actually quite large, and can fit most of your t-shirts and such.
While packing, make sure that you put all your liquids/makeup in a pouch and put it right on top. This way, you can access it easily when at the security check in the airport.