In this talk I will show you how to maximize your a-mean-ability. More precisely, I will survey some results about maximal amenable subgroups and subalgebras and share a new result which states that it is possible for the space of maximal amenable extensions to be any k-simplex (such as a triangle!). While this talk will technically be about operator algebras, it will be accessible to anyone who knows a bit of group theory (semi-direct products, free products, and the left regular representation).