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I have a requirement to overlap the colors so that they look a bit appealing. For now they can be seen with clear boundary between them. Please suggest how can I overlap the colors
You could use vertex colors.
Or you could do the fading by hand, you'd need to make an object for each color (or duplicate the mesh) and then move the UVs on an alpha texuture so you get gradients where you want them.
Or of course you can use cycles: