A doctor is so familiar with most of the things that can happen to minds and bodies that little can startle him.
Could you tell me if the underlined that is a relative pronoun or conjunction? I have a notion that it is a conjunction: little(=S) can startle him(=VP).
A relative pronoun refers to a noun or pronoun in the matrix clause.
A doctor that is very experienced is so familiar with most of the things that can happen to minds and bodies that little can startle him.
The first "that" obviously refers to "doctor."
The second "that" obviously refers to "things."
Try to find the noun that is the referent for the third "that."
Comments
A doctor is [so familiar with most of the things that can happen to minds and bodies that little can startle him].
"That" is a subordinator (your conjunction) introducing the bracketed declarative content clause functioning as a complement.
It's called an 'indirect complement' because although it follows the head noun it is actually licensed by the "so" that modifies "familiar".
In simple terms, "so" is in construction with "that".