get start

import drag-drop.js file to your page

const testData = [
  {
    "MONTH": "2",
    "TIME": "15:00",
    "TEXT": "Blah",
    "category": "A"
  },
  {
    "MONTH": "1",
    "TIME": "14:21",
    "TEXT": "Blah",
    "category": "B"
  },
  {
    "MONTH": "1",
    "TIME": "14:21",
    "TEXT": "Blah",
    "category": "B"
  },
  {
    "MONTH": "4",
    "TIME": "13:00",
    "TEXT": "Blah2",
    "category": "A"
  },
  {
    "MONTH": "6",
    "TIME": "10:00",
    "TEXT": "Blah3",
    "category": "B"
  },
  {
    "MONTH": "7",
    "TIME": "10:00",
    "TEXT": "Blah3",
    "category": "B"
  },
  {
    "MONTH": "4",
    "TIME": "13:00",
    "TEXT": "Blah4",
    "category": "A"
  },
  {
    "MONTH": "6",
    "TIME": "10:00",
    "TEXT": "Blah4",
    "category": "B"
  },
  {
    "MONTH": "7",
    "TIME": "10:00",
    "TEXT": "Blah5",
    "category": "A"
  },
  {
    "MONTH": null,
    "TIME": null,
    "TEXT": null,
    "category": "A"
  }
]
let table = $('#tableId').DataTable({
  'createdRow': function (row, data, dataIndex) {
    $(row).attr('category', data.category);
    if (data.category == "A") {
      $(row).attr('draggable', true);
    }
  },
  data: testData,
  serverSide: false,
  ordering: false,
  columns: [{
    data: 'MONTH',
  }, {
    data: 'TIME',
  }, {
    data: 'TEXT',
  }]
});

let selector = '#tableId';
let dragDroppable = new TableDragAndDrop(selector, testData, table);

Drag-drop-datatable

This is drag-drop plugin for datatable
We can to drog and drop siggle row or more rows on datatable
There is one point we should to pay more attentions

'createdRow': function (row, data, dataIndex) {
     $(row).attr('category', data.category);
         if (data.category == "A") {
             $(row).attr('draggable', true);
          }
      }

As the code writed ,drag-drap single row or more rows is based on category properties
IF all of the rows are same category, we only can drag-drop single row
IF some rows category properties are "A" and some rows category properties are "B",so we think category "B" rows Are belong to category "A" rows,so we can drag-drop more rows