Result:

1. First you need an image to make your Multi-Colored Effect on, I will be using this image:

2. Now that you have your render/picture or whatever, lets get started. Lets get us a color that we want to use to blend, I will use Red #FF0000. But you don't have to use this color.

3. Next we will make a new layer, ABOVE all color balanced Layers.

4. Now make that layer as SOFT LIGHT. Like so:

5. Now get your Brush tool (B) and pick a soft grunge brush so that the colors blend in nicely. I will use Rust 'n Grunge from this link

6. Now brush, preferably from the one of the sides. If you find that you brushed too much you can always lower the opacity.

7. Now you can stop here, but if you want to add more detail and more blending you can always go farther by doing the same steps from 1-6 with a DIFFERENT color. I went on with 3 different colors and lowered the opacity of the blue abit so that red and yellow can be my main colors.

8. Now once you've finished that, you can (OPTIONAL) add a color balance layer over all of the layers Layer>New Adjustment Layer> Color Balance. And you can play with the settings. If you don't like the result of the first color balance then you can always add another Color Balance Layer.

This concludes our tutorial, you should have something similar to this:

Some more examples using this tutorial: