Meditate on the following. Make sure you fully understand it before putting it into production code. Writing the explanatory comments is left as a mandatory exercise for the reader.

use strict;
use warnings;

use BaseModule qw( function1 function2 );

{
    no warnings 'overriden'; # I think that's the right one.

    my $old_function1 = \&function1;
    *function1 = sub {
        print "I am the overriden function\n";
        $old_function1->( @_ );
    };
}
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