He made four pastoral visits while serving as the archbishop. In 1951 he offered his resignation to Pope Pius XII though the pope refused it. But a compromise was later reached in 1954: Ermenegildo Florit was made the coadjutor so that he could aid Dalla Costa in his episcopal duties as the aged prelate grew ill.
During his tenure as archbishop, he made four pastoral trips. In 1951, he offered to step down from his position to Pope Pius XII, but the pope refused. Eventually, a compromise was reached in 1954: Ermenegildo Florit was appointed coadjutor, allowing him to support Dalla Costa in his duties as bishop, as the older prelate's health began to decline.