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Blender doesn't have an hard light blend type. I thought it would maybe be possible to get a similar result with multiple nodes.

Here is the source image:

enter image description here

And the result wanted when adding red:

enter image description here

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Blender cannot work with a majority of the original AdobePDF blend mode types as they are strictly display referred and fail miserably when operating on scene referred imagery.

From the AdobePDF specification, where cb is background and cs is source.

Multiply (cb, 2 * cs), if cs ≤ 0.5 Screen (cb, 2 * cs – 1) if cs > 0.5

As you can see, the "minus one" portion, as well as the screen operation, will yield completely erroneous results on scene referred imagery.

Also, 0.5 comparison values would be on display referred nonlinear imagery, which would be post display referred transform.

Ultimately, it is a meaningless blend mode within a raytracing context. You could of course write your own screen node as well as hard light, generate a display referred output, and try to hack something together. It would seem that more optimal approaches might be wiser than a hacked mess, however.

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How about simply mixing with a Color Ramp between tinted (generated by Multiply) and non-tinted images. Vary the color ramp for harder/softer edges and to vary the amount of highlight/strength of highlight (by changing the greyness of the Black/White color ramp colors).

compositor nodes

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    $\begingroup$ Why the downvote? This answer provides a method of taking the ‘original’ image as supplied in the question and producing a result very similar to the stated desired result using Compositor nodes (question is tagged with “Compositor”). $\endgroup$ – Rich Sedman Oct 24 '18 at 21:48
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You can achieve this result by increasing your global illumination strength and adding a color to it.

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