While HTTP technically does support multiple files in a single response through MIME-Multipart, browser support is mostly non-existent.
A possible course of action would be to add each generated PDF to a ZIP archive, and serve the ZIP file as the response instead:
$zip = new ZipArchive();
$zipFile = tempnam('/tmp', 'zip');
$zip->open($zipFile, ZipArchive::CREATE);
for ($i = 0; $i < 10; $i++) {
$mpdf = new mPDF();
$mpdf->WriteHTML('<p>Only test$i</p>');
$pdfData = $mpdf->Output("", \Mpdf\Output\Destination::STRING_RETURN);
$zip->addFromString("Document_name{$i}.pdf", $pdfData);
}
$zip->close();
header("Content-type: application/zip");
header('Content-Disposition: attachment; filename=Documents.zip');
readfile($zipFile);
unlink($zipFile);
exit;