my %filehandles;
sub open_file {
    my( $filename ) = @_;
    if( ! $filehandles{ $filename }) {
        open $filehandles{ $filename }, '>>', $filename
            or die "Couldn't append to '$filename': $!";
    };
    return $filehandles{ $filename }
}

...

my $fh = open_file( 'path1' );
print $fh "Hello\n";
my $fh2 = open_file( 'path1' );
print $fh2 "world!\n";