> s/cat/++$i/ge

interestingly it's possible to avoid /e in an efficient inside-out (TIMTOW) loop version of m///

say pos($txt) while $txt =~ m/cat/g

Now with s/// this kind of works, but isn't efficient because pos will be reset each time

use v5.12;
use warnings;
use Data::Dump qw/pp dd/;

my $txt = <<'___';
cat
dog
cat
mouse
eel
cat
housecat
catamaran
fish
___


say 'm-pos:', pos($txt) while $txt =~ m/cat/g;


my $cnt=1;

while ($txt =~ s(cat)($cnt)x) {
    say "s-pos:", pos($txt) // "undefined";
    $cnt++;
}

say $txt;
[download]

m-pos:3
m-pos:11
m-pos:25
m-pos:34
m-pos:38
s-pos:undefined
s-pos:undefined
s-pos:undefined
s-pos:undefined
s-pos:undefined
1
dog
2
mouse
eel
3
house4
5amaran
fish
[download]

and no, using s///g would do the outer loop only once, tho there might be a way to force a single replace with (?FAIL) ... probably?