I'm going to use this answer as a jumping board for others who can answer more precisely (if they choose not to close the question as nearly a duplicate of some others).
Indeed, some "flavours of negation" involve replacing the "vanilla" pas and others don't.
Je ne pense pas. I don't think.
You gave some good examples of negations that replace pas :
Je ne pense à rien. I'm not thinking about anything.
Je ne pense à personne. I'm not thinking about anyone.
Je ne pense jamais. I never think.
Je ne pense plus. I don't think anymore.
Here are some that don't:
Non, je ne pense pas non plus. I don't think either (=besides whatever else I don't do).
Je ne pense pas du tout à elle. I don't think about her at all.
Je ne pense pas encore à ce problème. I'm not thinking about that problem yet.
You asked why pas is not replaced in cases like these. The real question might be why it is replaced in the others (which are the majority — there are lots more not cited above).
French negation began with ne. That was sufficient to negate a verb. Whatever comes after the ne began as an adverb to qualify the negation (which is why it follows the verb).
If I recall correctly, pas, which as a noun means "a step", was introduced with the sense of "not even one step", that is, "not even a little bit". (Compare its etymology here — it only started being used in negatives in the 12th century.)
Gradually, because systematic exaggeration tends to weaken a word, the use of pas led to its no longer being emphatic, just becoming part of the default way to negate something. (In formal language, you can still omit it; in familiar language, you can instead drop the less salient ne now.)
The question therefore likely has to do with which other negations grew up alongside pas historically, as just other qualifiers that could be fitted in instead of pas before it was solidified, versus negations that grew up after pas was established as a necessary part of the negation. A quick check of personne, jamais, and rien suggests that they were contemporary with pas as matches for ne, whereas encore seems to have examples in the negative from only about 200 years ago, long after pas was established.
Another possible line of reasoning is the need to contradict the positive meaning that a word would have without pas. Notice that encore in the positive usually means still or, in some constructions, again. It may be that unlike the other terms that are more inherently negative (at least at this point in history), encore still needs an explicit pas to pick between its meaning. (You'd think that ne would serve to distinguish them, but as I mentioned above, ne is frequently dropped in familiar speech.)
Again, I invite clarifications/corrections from other editors!