Using the closeDialogAsync() function you can now open one dialog right after another

fixedMultipleDialogs.js

var i = 0;
function displayDialog() {
  var url = "https://localhost:3000/test.html";
  Office.context.ui.displayDialogAsync(url,{height:20, width:30, displayInIframe:true},
      function (asyncResult) {
          var dialog = asyncResult.value; // get the dialog
          var error = asyncResult.error;
          if(dialog == undefined && error.code > 0) {
            // log the error
            console.log(error.message);
          } else {
            // attache the events
            dialog.addEventHandler(Office.EventType.DialogEventReceived, function (arg) {
              // close this dialog, open the next
              dialogCloseAsync(dialog, function() {
                i++;
                if(i<4) {
                  displayDialog();                        
                }
              });
            });
            dialog.addEventHandler(Office.EventType.DialogMessageReceived, function (arg) {
              // close this dialog, open the next
              dialogCloseAsync(dialog, function() { 
                i++;
                if(i<4) {
                  displayDialog();                        
                }
              });
            });
          }
      });
}