It is a question about phrasal verbs related to perspective

I In the first case there is no phrasal verb "to take into" even if "to take into jail" werre idiomatic, and it is not; "to take into custody" is (ngram) but you should say "taken to jail"; the verb is not a phrasal because "into" is simply a preposition and the meaning is not modified by this preposition. This meaning is "to go with somebody from one place to another, especially to guide them or to lead them", a standard meaning, not considered that of a phrasal verb (ref., n° 2). Moreover, do not confuse this use of "to take to" with the phrasal verb "take to" (OALD).

II This seems to be correct (ngram) but the meaning of "up" is not clear, not to me at least. This is so because "up" is used to mark a state of finality in the processes, a state which is not explicit in "more". Here again, you are not dealing with a phrasal verb; it's just a matter of "coming somewhere with something or someone", a standard meaning (ref., n° 1); do not confuse this form with the phrasal verbs "to bring up" meaning " (ref., 6 meanings). Here, the use of "up" seems to be the same as in "They ate it up.", which means that they ate it till they finished it; the plain meaning is what you are dealing with again: "up" does not change this plain meaning and merely adds a precision. However, as I already said above, that doesn't seem compatible with "more", which confers no idea of finality but only that of a possible continuation.
Also, as can be seen in the references for the ngram, what is claimed by user Weather Vane in a comment seems right: jail is not a higher place. A lot of uses relative to the ngram above have for context bringing material and troups to the front line, this position being indubitably considered to be higher place; this shows that there exists a definite use for this sense of "up" with "bring", but I see no other. Only a modification such as a change of "more" for "the rest of" could perhaps justify fully "to bring up".