I created the overlapping circles pattern with black and blue, the used a Recolour Adjustment to get black and mauve.
I increased the size of the pattern, used a Recolour Adjustment to get black and red, then Contrast Negate layer blend mode to get white and turquoise.
Here is my first attempt. I kept black in all the sets of circles, but removed the inner circles to show more colour. Also, I changed the size of circle sets by removing outer circles rather than reducing the size of the whole set. I don’t particularly like the colour combination, but couldn’t find a Recolour Adjustment I preferred.
I changed quite a few of the colours to make this version somewhat lighter and brighter.
The method of using four copies and placing them in the corners is easy in a way, but I found it difficult to get a good result because it is almost impossible to predict what will happen when the images overlap in the centre.