Using amalgamated free products of lamplighter groups, we construct masas that have exactly k maximal amenable extensions which are factors. Moreover, in this setting we are able to identify the k-simplex with the space of all maximal amenable extensions. The proof uses the concepts of simultaneous relative asymptotic orthogonality, an extension of relative asymptotic orthogonality, and the uniform flattening strategy, which was introduced by the authors in a previous paper to compute lower bounds on sequential commutation path lengths. This work is joint with Srivatsav Kunnawalkam Elayavalli.