Have Database Update ignore prefix for multisite with shared database
Looking at the comments in settings.php, you may well be able to do something like this:

$databases['default']['default'] = [
  'database' =&gt; 'db_name',
  'username' =&gt; 'root',
  'password' =&gt; 'root',
  'host' =&gt; 'localhost',
  'port' =&gt; '3306',
  'driver' =&gt; 'mysql',
  'prefix' =&gt; [
    'default' =&gt; 'shared_',
    'custom_table' =&gt; '',
  ],
];


I haven't tried it, but in theory that should set the prefix for all tables to shared_, except for the custom one, which would have no prefix.