how can several configuration files be used, with the same tests run for each config file ?

One way is simply to write your own loop.

for my $config_file (@LIST) {
    ok is_valid($config_file);
    # ...
    is $this, $as_expected;
}
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If you have three configurations in @LIST and two tests in your loop block, then just add six to your planned test count.

This is not very clever, but it gets you going, and with test suites, it's better to install something simple right away. You can always upgrade the cleverness later.