How do you get a loud sound (on saxophone) without losing a good tone?
What mouthpiece and reed (type and number) are you using?
I use a Yamaha mouth piece ( alto), A 1, and a 2 Rico reed
What you could do right now is try a harder reed, 2.5, maybe 3.
Let’s look at the space between the reed and the mouthpiece. The reed vibrates in that space. The more air you put through the horn, the more the reed will vibrate and the more sound you will create.
There is a limit to how much louder you can without sacrificing tone though. As you put more air through the mouthpiece, it means that the reed vibrates more distance, perpendicular to the airflow. Eventually that can make the space between the mouthpiece and reed close and as it gets closer to closing as well as going to its limits, the sound can become distorted.
To play louder you basically need to use a harder reed or a more open mouthpiece, both options require more pressure. You essentially need more power to play louder.
The less expensive option is to keep using your current mouthpiece and switch to a harder reed.
The more expensive option is to switch your mouthpiece. To get louder, you’ll want a more open tip and possibly a baffle or other characteristics. Metal mouthpieces tend to be designed to get more volume. To get louder, your sound may change. There are tradeoffs with designs.
You may find it’s harder to control your sound with a harder reed and/or a different mouthpiece. If you only have a bit of trouble with it, you can keep practicing and will likely adjust. If it seems completely out of control, you may be in a bad situation. Therefore, you probably should start with a different reed and if you want a new mouthpiece, you should try it before deciding it’s what you want.