Problems concatenating arrays by session

Question

I apologize in advance for the title, my question is not that easy to explain on it.

What I mean by that is the following:

Having an array of type, 4x4, it has 4 sectors like so.

Now I need to concatenate another 4x4 to it but the first line of it should go with the first sector, second one with the second sector and so on.

So to summarize I have something like this

1. 00:[(0, 1), (0, 2), (0, 3), (1, 0), (2, 0), (3, 0)] ->sector 1
2. 01:[(0, 0), (0, 2), (0, 3), (1, 1), (2, 1), (3, 1)] ->sector 1
3. 02:[(0, 0), (0, 1), (0, 3), (1, 2), (2, 2), (3, 2)] ->sector 2
4. 03:[(0, 0), (0, 1), (0, 2), (1, 3), (2, 3), (3, 3)] ->sector 2
5. 04:[(1, 1), (1, 2), (1, 3), (0, 0), (2, 0), (3, 0)] ->sector 1
6. 05:[(1, 0), (1, 2), (1, 3), (0, 1), (2, 1), (3, 1)] ->sector 1
7. 06:[(1, 0), (1, 1), (1, 3), (0, 2), (2, 2), (3, 2)] ->sector 2
8. 07:[(1, 0), (1, 1), (1, 2), (0, 3), (2, 3), (3, 3)] ->sector 2
9. 08:[(2, 1), (2, 2), (2, 3), (0, 0), (1, 0), (3, 0)] ->sector 3
10. 09:[(2, 0), (2, 2), (2, 3), (0, 1), (1, 1), (3, 1)] ->sector 3
11. 10:[(2, 0), (2, 1), (2, 3), (0, 2), (1, 2), (3, 2)] ->sector 4
12. 11:[(2, 0), (2, 1), (2, 2), (0, 3), (1, 3), (3, 3)] ->sector 4
13. 12:[(3, 1), (3, 2), (3, 3), (0, 0), (1, 0), (2, 0)] ->sector 3
14. 13:[(3, 0), (3, 2), (3, 3), (0, 1), (1, 1), (2, 1)] ->sector 3
15. 14:[(3, 0), (3, 1), (3, 3), (0, 2), (1, 2), (2, 2)] ->sector 4
16. 15:[(3, 0), (3, 1), (3, 2), (0, 3), (1, 3), (2, 3)] ->sector 4

And I want to sum with something like this:

1. 0:[(0, 0), (0, 1), (1, 0), (1, 1)]
2. 1:[(0, 2), (0, 3), (1, 2), (1, 3)]
3. 2:[(2, 0), (2, 1), (3, 0), (3, 1)]
4. 3:[(2, 2), (2, 3), (3, 2), (3, 3)]

I had no problems concatenating the tuples but I can't find a way to make the loop follow the desired path

Does anyone have any ideas on how to go about this?

EDIT: In the image, an example of the mentioned array.

Within each item, there is a list with tuples that I will add to my list of larger size

This is the larger list I'm referring to

So basically I want my 0 items to add to 00, 01. My 1 items to add to 02 , 03. And so on