Append data to localStorage object

I'm trying, unsuccessfully, to add a new object to a current localStorage object. Instead of, at the end, having two sets of data in localStorage, I get the last one. Any insight on what I'm doing wrong? Thanks

Here's what I'm trying to do:

// add the first student
var newStudent = [{
     "name":        "John",
     "age":         21,
     "nationality": "Spanish"
 }];

localStorage.setItem("students", JSON.stringify(newStudent));


// Retrieve the object from storage to add a new student
var retrievedObject = localStorage.getItem("students");
var stored          = JSON.parse(retrievedObject);

// add a new student
var newStudent2 = [{
    "name":        "Mary",
    "age":         20,
    "nationality": "German"
}];
var stored = Object.assign(stored, newStudent2);

// Update the storage
localStorage.setItem("students", JSON.stringify(stored));
var result = localStorage.getItem("students");

console.log(result);