Yes there is one line where we can do match out of the three lines and that line is the first line in three lines.

The following code uses an array as a "circular list" to delay the printing of the EXTRA. Is this what you need?

use strict;
use warnings;
my $match = qr /Match/;
my $extra = qq(EXTRA\nEXTRA\n);
my @extras = (q()) x 3;
my $in  = 3;
my $out = 0;
while (my $line = <DATA>) {
    $out = ($out+1) % 4;
    print $line, $extras[$out];
    $in  = ($in +1) % 4;
    $extras[$in] = ($line =~ /$match/)? $extra : q();
}
__DATA__
a
b
Match1
Match2
c
d
e
f
g
Match3
h
i
j
k
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Bill