The text animation presets work in the same way as other animation presets---they add layer properties, set keyframes or expressions for those layer properties, and set layer properties to specific values.
If you add one animation preset after another to the same layer, you run the risk of overwriting or modifying the layer properties set by the first with the properties set by the second.
If you want to create an animation that uses pieces from two different animation presets, I recommend applying one at a time, decomposing and studying each, and then putting the pieces back together yourself. This way, you'll also learn how to build animations of your own from scratch, instead of just relying on the presets.
Here's a tip from the animation presets section of After Effects Help:"A great way to see how advanced users use After Effects is to apply an animation preset, and press U or UU to reveal only the animated or modified layer properties. Viewing the animated and modified properties shows you what changes the designer of the animation preset made to create the animation preset."
Contrary to Todd I do not think that overwriting properties is the issue here - adding multiple presets usually simply adds another text animator group and increments the name. The bigger issue is, that even if in differnt groups, identical properties still interact and accumulate their values. If you have e.g. a per-character position in one group and a per-word position in the other, both position values will still be combined, making the letters inside the word act differently than in areas where the per-word animator is not applied. These behaviors can be controlled somewhat in the Advanced section of the animators by tweaking the mixing modes and ease settings, but generally a better way to solve the issue is to rip out one of the duplicate properties and adjust the remaining one to take over its functionality. Also note, that of course the timing of each individual animator also plays an important part, so simply moving or disabling keyframes may resolve such conflicts as well.
Thank you to both who answered my post. Both have given suggestions which give a path to expand my understanding. It is appreciated.
I hope this reply reaches you as I'm not sure how the forum works in that regard.