Instead of using a multine regex, you could consider looping over the lines in turn and removing every six lines where there's a match on the fourth.

I think the code is pretty self-explanatory (@lines contains your file):

my $i = 3;                             # from line 4 ...
while ($i < @lines - 2) {              # ... until last but 3
    if ($lines[$i] =~ m!<MYTAG></MYTAG>!) {
        splice(@lines, $i - 3, 6);     # kill 6 lines from $i - 3
    } else {
        $i++;
    }
}
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— Arien