Redefine macro without using tmp variable

This of course cannot work, because it will leave the effect of \begingroup hanging until you call \abc, which will probably happen in undesirable places (see your other question).

To me it seems you want to do

\def\abc{abc}
\expandafter\def\expandafter\abc\expandafter{\abc def}

but this is clumsy and limited to only allow appending.

Without reinventing the wheel, you can use etoolbox:

\documentclass{article}
\usepackage{etoolbox}

\newcommand{\abc}{abc}

\begin{document}

The macro \verb|\abc| expands to ``\abc''.

\appto\abc{def}

The macro \verb|\abc| expands to ``\abc''.

\preto\abc{X}\appto\abc{X}

The macro \verb|\abc| expands to ``\abc''.

\end{document}

This will print

The macro \abc expands to “abc”.
The macro \abc expands to “abcdef”.
The macro \abc expands to “XabcdefX”.

Reorganized and corrected my answer

The cause why \orgabc is still available is that the group is actually never closed, it causes warnings about semi groups.

Now, egreg has used \expandafter\def\.... already.

It is possible to use \xdef\foo{\foo other stuff} to use a shorter version.

As a third variant, apply \g@addto@macro from the LaTeX kernel, which stores everything expanded in a token first and redefines the macro with \xdef, in order to expand the token.

\documentclass{article}



\def\abc{abc}
\def\abcother{abc}
\def\abcyetanother{abc}
\expandafter\def\expandafter\abc\expandafter{\abc\ defappended which works}

\xdef\abcother{\abcother\ defappended works as well}

\makeatletter
\g@addto@macro\abcyetanother{\ and here again}

\makeatother


\begin{document}
First version: \abc

Second version:  \abcother

Third version: \abcyetanother
\end{document}