The most common and most likely answer to this crossword clue is the 2 plus 7 plus 3 plus 7 letter word GO THROUGH THE MOTIONS
I've seen this crossword clue in The Times
G
O
T
H
R
O
U
G
H
T
H
E
M
O
T
I
O
N
S
Buddy explains!
The straight part
We know that "Explore specific proposals, though somewhat mechanically" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case explore specific proposals, though somewhat mechanically = go through the motions.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.