Assuming you want some flexibility about your substitutions, you can use something like this:

use strict;
use warnings;

my @replace_by_level =(
  # Level 0 ----
  { "abc.net"        => "abcde.net",
    "something.else" => "Other.thing"},
  # Level 1 ---
  { cm  => "dm",
    dn  => "xx",
    ef  => "yy"},
  # Level 2 --
  { zero  => "one",
    one   => "two",
    two   => "three"},
  # Other levels as required ...
 );

my $orig_url = "https://abc.net/cm/one";

my ($transformed_url, $temp) = $orig_url =~m|(\w+://)(.+)|;

my $level=0;
$transformed_url .= join "/", map { $replace_by_level[$level++]{$_} } 
+split /\//, $temp;

print qq|$transformed_url\n|;     # https://abcde.net/dm/two
[download]

Checking whether the transformation exists, before applying it is left as an exercise.