Like this?

$exp->expect($timeout,
   [ qr/regex1/ => sub {
      my $exp = shift;
      ...
      $exp->send("response\n");
   } ],

   [ qr/regex2/ => sub {
      my $exp = shift;
      ...
      $exp->send("response\n");
   } ],
);

$exp->expect($timeout,
   [ qr/regex1/ => sub {
      my $exp = shift;
      ...
      $exp->send("response\n");
      exp_continue
   } ],
);
[download]

Alternatively,

$first = 1;

$exp->expect($timeout,
   [ qr/regex1/ => sub {
      $first = 0;

      my $exp = shift;
      ...
      $exp->send("response\n");
   } ],

   [ qr/regex2/ => sub {
      return exp_continue_timeout unless $first;
      $first = 0;

      my $exp = shift;
      ...
      $exp->send("response\n");
   } ],
);
[download]

Update: Part of my reply got accidently erased. Re-added the missing chunk.