Thus you desire to expand your falsetto voice. If you are male, fine. If you're female, you don't have to except you have to play a character role in a musical theater production.
Presently what is falsetto? Falsetto is a genuine, breathy tone on high notes. Think of it as pure head voice, with no few vibration or chest sound at all. An example some people have heard is a boy soprano. Women can attain the sound without much complexity once they learn to use their upper resonance. So, ladies, you don't have to read any further if you don't want to.
Falsetto is so termed because it was once believed to be created by the false vocal folds of the larynx. Modern laryngoscopy exhibited that it is in fact produced by the true vocal folds. When singing in falsetto the vocal folds are adulterated, stretched, and elongated so that they vibrate only at the margins. They do not fully close, which recommends the breathy quality.
It is hard to control dynamic changes (softness and loudness) on persistent notes when singing falsetto, because of the fruitless use of the vocal folds. Falsetto can be valuable when you're learning to use your head voice and upper vibrancy, but when you have learned that you should use it usually instead of falsetto.
If after reading the above you're still determined to develop falsetto, here is how to do it.
Start with a good warm-up routine, and make certain you're using good posture and breath support. Try to do again the sound of a boy soprano. Listen to a few recordings to get the idea of the tone you're striving to produce.
Go for a pitch in the upper part of your range. On a hum, sidle from your starting pitch up a fifth and back down: act upon. Keep your tone light and hoot. Try similar pitches on "nee" and "nah". Then, move up a half-step and do again the fifth slide up and down, again on the hum, "nee", and "nah". Keep on moving upward as far as you can without exertion.
During the exercises, have your face and mouth relaxed and clear of tension.
If you want to sing the high range with power and dynamics and you're not a natural tenor, you may bemore comfortable to have the song transposed to a lower key. If you can't improve the range without falsetto, maybe you just shouldn't be singing that range.
Falsetto can be used now and then for artistic effect in various songs, but it's not healthy to form a habit of it.