For enumerate there are options like start or resume or commands like \setcounter{enumi}{4} or \addtocounter{enumi}{41} as discussed in questions like How can I make an enumerate list start at something other than 1? or Resuming a list.
Are there analogous possibilities for the parts environment in the exam document class?
\documentclass{exam}
\begin{document}
\begin{questions}
\question[10]
Some not indented text
\begin{parts}
\part this should be (a)
\part this should be (b)
\end{parts}
Some more not indented text interrupting the parts
\begin{parts}
\part this should be (c)
\part this should be (d)
\end{parts}
\end{questions}
\end{document}