You can use closures to do it:

# generate a closure:
sub gen_change_mode {
    my $mode = shift;
    return {
        # same code as in change_mode

    };
}

# then do this
$main->Button(-text => 'To Upper Case',
    -command => gen_change_mode(2)
    )->pack;

# or this
$some_ref = gen_change_mode(3);

$main->Button(-text => 'To Mixed Case',
    -command => $some_ref
    )->pack;
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so in the last case gen_change_mode(3) will return a code reference with $mode set as 3, meaning you can pass this around as a code ref, which is what you're after.

there is an example in `perldoc perlref` which uses a lexical (my) var inside the anon sub that gets returned, so you can pass more arguments to it when you finally run it as a subroutine.