This may be misunderstanding your issue but amsart uses multiple
\author commands to add each author, the relevant packages called by the document class then combine these as is set by the AMS preferences. The instructions to authors on CTAN (https://www.ctan.org/pkg/amsart) provide a concise but relatively straightforward guide. Inserting the following code before
\maketitle should have the desired effect
When one then uses the
\maketitle command all
\author entries (and appropriate author details). There are some discussions on customising amsart titles on here amsart option titlepage puts the address on the last page and Authors in amsart but again as barbara beaton commented, customising will not in general be a trivial task as noted by barbara beeton.
An alternative, similar documentclass to look into could be revtex (which is used for APS journals), which offers a wide range of journal styles but is no more customisable.