If 5 people come together and form a music band, is that band just that 5 people or something external? That's what EU is, 27 states who send people to do stuff

If 5 people come together and form a music band, is that band just that 5 people or something external? That's what EU is, 27 states who send people to do stuff that concern all the member states in Brussels. You can load as much meaning as you like on top of it, but there's no external party. The president of the EU commission(there's no president of EU) is elected by the heads of the governments(the EU member state governments, elected by the people of that state) and approved by the EU parliament(directly elected by EU member state citizens). So, If one of the band members is elected by the other band members to be the lead singer, is that band member something external?