Using Duel Sim/eSim for IPhone SE 2020

I’m currently with AT&T Wirleless, as I recently upgraded to the IPhone SE 2020. When I made the switch, I also essentially had to decide to join my family’s mobile plan...So I figured that it would be worth that “minor detail” as to be able to get and own the new phone. (and to be extremely honest it is) But, I’ve obviously had to give up a few things (freedoms and such) that I hadn’t really considered. Maybe small things...but if I want to go on to my Provider’s app or website and order something now....Its basically a family decision...So my question, is… Could I rectify this by activating another account/new additional number (eSim) and if so? Would I have to do it through AT&T, or could I literally use any other service (cell) provider? I then have that account separately and in my name only?