\documentclass{article}

\usepackage[enable-debug]{expl3}

\usepackage{groupthm}


\ExplSyntaxOn

\AppendToTheoremGroup[prefix = n]{all}
\AppendToTheoremGroup[suffix = n]{all}

\DeclareTheoremGroupRule[suffix]{all}{higher}{dagger}
\DeclareTheoremGroupRule[suffix]{all}{higher}{star}

\NewTheoremGroup [ suffix   = { *             } ] { star       }
\NewTheoremGroup [ suffix   = { $^{\dagger}$  } ] { dagger     }

\NewGroupedTheorem*[group = {star, dagger} ]{theorem}

\NewGroupedTheoremFamily[ group = { dagger, star }, starred ~ version = false] {example}

\NewGroupedTheoremFamilyOptions{example} { s t+ }
  {
    \IfBooleanT { #1 }
      {
        \AddTheoremToGroup { star }
      }
    \IfBooleanT { #2 }
      {
        \AddTheoremToGroup { dagger }
      }
  }

\RenewGroupedTheoremFamilyOptions{example} { s t+ } {}



\ExplSyntaxOff

\begin{document}

\begin{theorem}
  test
\end{theorem}

\begin{theorem*}
  test  
\end{theorem*}

\begin{example}
  test
\end{example}

\begin{example}*+
  test
\end{example}

\begin{example}*
  
\end{example}

\begin{example}+
  test
\end{example}



\end{document}