The logic of supreme being disallows there being more than one. Grammatically, 'supreme' is a superlative, not a comparative. Thus the vocal group, The Supremes, might strike the logically persnickety as misnamed. How can each each gal be supreme when there are three of them? (That Diana Ross thought herself 'more supreme' than the others cuts no ice.)
You can guess where I am going with this. God is the supreme being. Christians believe that God is triune, one God in three divine Persons. If each Person is God, and God is supreme, then each Person is supreme. But the Son proceeds from the Father, and the Holy Ghost from the Father and the Son (filioque). Since the Father begets the Son, is the Father 'more supreme' than the Son?
Divine supremacy is supremacy in respect of all 'great-making properties' (A. Plantinga) or perfections. But if the Father begs the Son, then the Father is superior to the Son in respect of ontological primordiality. It follows that the Son is not supreme in respect of all perfections. Similarly for the Holy Ghost.
Is there a serious problem here, or not? You will note that this is a close cousin of my aseity puzzle.