Yes, it is possible:

BEGIN {
    *CORE::GLOBAL::require = sub {
        my $file = shift;
        $file =~ s,^My/,Another/,;
        CORE::require($file)
    };
}

use Data::Dumper;
use My::Foo;
[download]

I think the important part is that the CORE::GLOBAL::require function must be imported into the namespace, not just defined. This makes some difference in how the GV entry looks, but I cannot remember why this is or was important.

It becomes somewhat more complicated if you want to get the error messages right as well (you have to use string eval() for the CORE::require() call and prefix the call inside the string with a #line directive with information from caller()).