Possible Clues:

• Show tune with the repeated line 'Come to me, come to me!'
• South Pacific song
• 1949 show tune with the lyric 'Here am I, your special island!'
• “Here am I, your special island” show tune
• ''South Pacific'' tune
• Its sung in the same act as 'Some Enchanted Evening'
• Its sung in the same act as "Some Enchanted Evening"
• 'South Pacific' show tune
• 'There Is Nothin' Like a Dame' follower