By all means, yes! But, you cannot do it by using a "falsetto" head voice. You must learn to navigate your voce in piena testa, or legitimate head voice. This is just like your chest voice in regard to your true vocal folds vibrating while pressed together. Contrary to what some think, it is not a 'mixing' or 'blending' of head and chest voice. Instead, it is a relaxation of the thyroarytenoid muscles (the thick muscles that make up the vocal folds) with a tightening of the cricothyroid muscles (the muscles that connect to the arytenoid cartilages that elongate the vocal folds -- making higher pitches). When this is done, one can extend the chest voice sound into the upper range of their voice beyong their "calling voices". Too much thyroarytenoid usage will result in cracking and strain. To do it in practice is tough to learn. I have found that the easiest way to do it is to sing "ee" vowel in chest voice and slide it up higher until it breaks. This is your "break point". Above this lies you true head voice. You must learn how to use the chesty "ee" sound beyond your break point without straining the voice, yet making a loud, resonant sound. DO NOT USE FALSETTO, as this will inhibit your vocal strength and ability to hit voce in piena testa. (for men, anyway) Really, you need to hire a good voice teacher. It is tough to learn, and you can easily damage your voice permanently without the aid of a trained professional singer./

You need to find a different way of singing those higher notes. There's a good exercise for this called the siren, where you start with your lowest note, slide up to your highest and back down to your lowest. On the way up and down a beginner may encounter some 'breaks' (gaps where you jump a few notes as the different set of muscles kick in). Let this happen. With regular practice of this exercise the breaks get smaller as you learn to gradually let go of one set of muscles and bring the next set into use. Try and maintain the same tone throughout but never strain or tense your throat, the whole exercise should feel relaxed and easy.