It's trivial by wrapping part of your code in a for() loop, and turning the single scalar $URL link into an array @URLS, that contains a list of urls instead. The for() loop iterates over this list. Note that this assumes the regex is the same for all urls. Untested:

use strict;
use warnings;
use LWP::Simple;

my @URLS = qw(
    http://one.example.com
    http://two.example.com
    http://three.example.com
);

my $regex   = '<div class="usertext-body may-blank-within md-container
+ ">' .
              '<div class="md">(.+?)</div>\s*</div>' .
              '</form><ul class="flat-list buttons">';

for my $URL (@URLS){
    my $CONTENT =  get($URL);
    my $x       = '';
    my $count   =  0;
    
    while ($CONTENT =~ m{$regex}gs){
        $x .= $1;
        ++$count;
    }

    print "---$URL---\n";
    print $x; 
    print "Count: $count\n";
}
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