Using thmtools: numbering with asterisk

Question

I would like to repeat a theorem number with an added asterisk. That is, the original theorem is:

Theorem 1. Lorem ipsum...

And I would like the analogue theorem to be:

Theorem 1*. Lorem ipsum...

Answer 1

Here's one possibility:

\documentclass{article}
\usepackage{amsthm}
\usepackage{thmtools}

\declaretheoremstyle[
  spaceabove=6pt, 
  spacebelow=6pt,
  headfont=\bfseries,
  notefont=\mdseries, notebraces={(}{)},
  bodyfont=\itshape,
]{mystyle}

\let\variant\relax

\declaretheorem[style=mystyle]{theorem}

\declaretheorem[
  name={Theorem~\variant{$^\ast$}},
  style=mystyle,
  numbered=no,
]{theorem*}

\newenvironment{rtheorem}[1]
  {\newcommand\variant{\ref{#1}}\begin{theorem*}}
  {\end{theorem*}}

\begin{document}

\begin{theorem}
A test regular theorem.
\end{theorem}

\begin{theorem}[Euler's identity]
\label{thm:euler}
$e^{i\pi} + 1 = 0$
\end{theorem}

\begin{theorem}
Another test regular theorem.
\end{theorem}

\begin{rtheorem}{thm:euler}[Euler's identity revisited]
$e^{i\pi} = -1$
\end{rtheorem}

\begin{theorem}
Yet another test regular theorem.
\end{theorem}

\end{document}

The central idea is to use the \label, \ref mechanism for a variation of a previously stated theorem. The "regular" theorems are produced using the theorem environment; a variation of a given theorem is produced using the rtheorem theorem which has as mandatory argument the string used to label the original theorem (both environments admit the default optional argument).