if the u. s. government were seeking broader powers not clearly specified in the constitution, under which clause of the u. s. constitution would such additional authority be granted?

The name of the clause is the "Necessary and Proper" clause. This clause, also known as the elastic clause, allows the United States federal government to obtain powers not specifically written in the constitution. This idea of obtaining powers not specifically written in the constitution is known as an implied power. This concept has been used several times throughout American history, including Thomas Jefferson's purchase of the Louisiana territory from France.