(A) You possibly/probably should
(B) You should possibly/probably
I'm more used to the latter (the ones in B), but can I have a couple of examples for the first one (the ones in A)?
In most cases adverbs (possibly/probably) come after the verb.
The choice of (A) would be appropriate if you wish to emphasize or stress something.
Note! Here, the word order of choice (A) is appropriate: