You should create a sub-routine that handles these for you. For example:

sub mprint
{
        my @fh;
        push(@fh, shift) while (ref($_[0]) eq 'GLOB');

        print $_ @_ foreach (@fh);
}

open($so, ">&STDOUT");
open($se, ">&STDERR");

mprint $se, $so, "This tests\n";
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It's not quite as clean as the builtin, but it's pretty close. You could even group your filehandles together into array packages, so that it's tidier:

my @default = ($so);
my @log_and_print = ($log, $so);

mprint @default, "Standard message\n";
mprint @log_and_print, "This goes to log and screen\n";
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Update:
IO::Tee looks like a great way to do this as well, provided you can install your own modules.