Are 'take up' and 'pick up on' interchangeable?
in these following two sentences?
I'd like to pick up on your last comment.
I'll take up the story where Tim had left off.

Question

Answer

In most cases the answer is no, but there is one exception. Info from the Oxford Advanced Learner's Dictionary:

take something  up
8) to return to an earlier subject or situation in order to continue it

pick up on something
2) return to a point that has already been mentioned or discussed

Note that use #8 of take up something is the same as use #2 of pick up on something.

Answer

I see you've added examples. Those suit the dictionary entries I posted about.