Command that changes its definition the nth time it's used

Have a look at the following example:

\documentclass{article}

\newcounter{testcount}

\newcommand{\modifyme}{%
\addtocounter{testcount}{1}
\ifnum\thetestcount<3%
    Hello 
\fi
\ifnum\thetestcount>2%
    World
\fi
}

\newcommand{\resetme}{\setcounter{testcount}{0}}

\begin{document}

\modifyme

\modifyme

\modifyme

\modifyme

\resetme

\modifyme

\end{document}

I love using counters! Here only the expansion after the number specified in \changedefinitionafter is modified.

\documentclass{article}
\pagestyle{empty}% for cropping
\makeatletter
\newcount\count@foo
\newcount\nth@foo
\newcommand\changedefinitionafter[4]{
    % #1: name of macro
    % #2: exceptional occurence
    % #3: normal expansion
    % #4: exceptional expansion
    \global\count@foo=0
    \global\nth@foo=#2
    \gdef#1{%
        \advance\count@foo by 1
        \ifnum\count@foo=\nth@foo
            #4%
        \else
            #3%
        \fi
    }
    \edef\resetname{reset\expandafter\@gobble\string#1}
    \expandafter\gdef\csname \resetname \endcsname{\global\count@foo=0 }
}
\makeatother
\begin{document}
\obeylines
\changedefinitionafter\foo{3}{OneTwoThree}{Next}
\foo
\foo
\foo
\foo
\resetfoo
\foo
\foo
\foo
\foo
\end{document}

No counter, but three macros for each command of this type:

\documentclass{article}

\makeatletter
\newcommand{\newchangingcommand}[4]{%
  % #1 = macro name
  % #2 = steps
  % #3 = value until step #1
  % #4 = value from step #1
  \@namedef{\string#1@counter}{0}%
  \@namedef{\string#1@limit}{#2}%
  \def#1{%
     % step the counter
     \global\@nameedef{\string#1@counter}{\number\numexpr\@nameuse{\string#1@counter}+1\relax}%
     \ifnum\@nameuse{\string#1@counter}=\@nameuse{\string#1@limit}\relax
       \gdef#1{#4}#4%
     \else
       #3%
     \fi
  }%
}
\providecommand\@nameedef[1]{\expandafter\edef\csname#1\endcsname}
\makeatother

\newchangingcommand{\foo}{3}{Two}{Next}
\newchangingcommand{\foob}{2}{One}{Next}

\begin{document}

\foo--\foob\par
\foo--\foob\par
\foo--\foob\par
\foo--\foob\par

\end{document}

Be aware that using such commands in moving arguments will fail for several reasons.