How to add values to Firebase Firestore without overwriting?

There are two ways in which you can achieve this. First one would be to use a Map:

Map<String, Object> map = new HashMap<>();
map.put("yourProperty", "yourValue");
firebaseFirestore.collection("Users").document(user_id).update(map);

As you can see, I have used update() method instead of set() method.

The second approach would be to use an object of your model class like this:

YourModelClass yourModelClass = new YourModelClass();
yourModelClass.setProperty("yourValue");
firebaseFirestore.collection("Users").document(user_id)
    .set(yourModelClass, SetOptions.mergeFields("yourProperty"));

As you can see, I have used the set() method but I have passed as the second argument SetOptions.mergeFields("yourProperty"), which means that we do an update only on a specific field.

I suggest you to add one more document or collection that it will be able to store more just one data values for single user.
You can create a document references for both activities:

firebaseFirestore.collection("Users").document(user_id+"/acitivity1").set(data);
//and  
firebaseFirestore.collection("Users").document(user_id+"/acitivity2").set(data);

Or you can create a sub-collection for it:

firebaseFirestore.collection("Users").document(user_id)
                  .collection("Activities").document("acitivity1").set(data);
//and
firebaseFirestore.collection("Users").document(user_id)
                  .collection("Activities").document("acitivity2").set(data);

More about hierarchical data there.