In most browsers, you cannot open multiple print dialogs. Instead, you can open them sequentially. The easiest way to print PDFs in Javascript is with PrintJS

Here's a recursive example that prints an array of PDFs.

var documentURLs = ["https://example.com/pdf1.pdf", "https://example.com/pdf2.pdf"]
function printDocuments(index){
   if(index > documentURLs.length){
        return;
   }
   printJS({
     printable: documentURLs[index],
     type: 'pdf',
     onPrintDialogClose: function () {
        printDocument(index+1)
     }
   })
}

You'd start it with printDocuments(0). Be sure to download and include the PrintJS library with <script src="print.js"></script>