Fußnoten in Beamer auf selbe Folie?

\documentclass{beamer}

\makeatletter

\def\beamer@autobreakframebox{%
  \global\setbox\beamer@splitbox=\box\voidb@x%
  \ifbeamer@autobreak%
    % Ok, frame was overful -> split it!
    \setbox\@tempboxa=\vsplit\beamer@framebox to\beamer@autobreakfactor\textheight%
    \global\setbox\beamer@splitbox=\box\beamer@framebox%
    \@tempdima=\ht\beamer@splitbox%
    \ifdim\@tempdima<\beamer@autobreaklastheight%
      \global\beamer@autobreaklastheight=\@tempdima\relax%
    \else%
      \setbox\@tempboxa=\vbox{\unvbox\@tempboxa\unvbox\beamer@splitbox}%
      \global\setbox\beamer@splitbox=\box\voidb@x%
    \fi%
    \setbox\beamer@framebox=\vbox to\textheight{\unvbox\@tempboxa%
      \vskip\beamer@framebottomskipautobreak%
      %\ifvoid\beamer@splitbox% <-- Commented
        \ifvoid\beamer@footins%
        \else%
          \begingroup
            \usebeamercolor*[fg]{footnote}%
            \footnoterule%
            \unvbox \beamer@footins%
            \global\setbox\beamer@footins=\box\voidb@x%
          \endgroup  
        \fi%
      %\fi% <-- Commented
      \beamer@exitcode%
    }%
  \else%
    \setbox\beamer@framebox=\vbox to\textheight{\unvbox\beamer@framebox%
      \vskip\beamer@framebottomskip%
      \ifvoid\beamer@footins%
      \else%
        \begingroup
          \usebeamercolor*[fg]{footnote}%
          \footnoterule%
          \unvbox \beamer@footins%
          \global\setbox\beamer@footins=\box\voidb@x%
        \endgroup 
      \fi%
      \beamer@exitcode}%
    \global\setbox\beamer@footins=\box\voidb@x%
  \fi%
  }

\makeatother

\begin{document}

\begin{frame}[allowframebreaks]
  \begin{itemize}
  \item Item\footnote[frame]{First frame footnote}
  \end{itemize}
  \input knuth
  \input knuth
  \begin{itemize}
  \item Item\footnote[frame]{Second frame footnote}
  \end{itemize}
\end{frame}

\end{document}