Basically, I think each animation/setting is saved per-character. So to create this, do this:
1. Add your text in the Text+
2. Go to the first frame of the animation
3. Add the CLS, and in the CLS modifier right-click on "Right-click here to animate.." and choose Animate
4. In the Viewer, select the line of text (or group of characters) to be animated
5. In the CLS modifier, apply the shading/parameters you want on this frame
6. Go to the next frame in the animation
7. In CLS, apply the shading/parameters you want on this frame
8. Repeat steps 5 - 7 for each keyframe for this set of characters / this line
9. Repeat steps 4 - 8 for each separate group of characters - eg once per line of text.
There are a couple of downsides:
1. When selecting in the viewer, you need to select characters based on their initial, non-CLS position. So when you're animating position, it can create situations like this, where if you want to later modify the animation you need to select the characters based on where they were, not where they're now animated to:
I've selected all four lines of text, but I have to do this in the positions they were in before I applied CLS adjustments. I can't select the text based on where I can actually see it, as the CLS has already adjusted its position.2. There's no visualisation in the modifier or the Spline Editor as to how many separate sets of animations you have. In my example above I created two keyframes - one on frame 0, one on frame 100 - for each of four lines of text. In the Spline Editor I see have two keyframes, but there's no indication as to which characters are animated on these keyframes:

So there could be some advantage to using multiple Modifiers - or even multiple Text+. It would at least make it easier to understand what characters are modified by what and when.