Single-column framed minipage spanning two or more slides in Beamer

Question

I searched and could not find an easy non-labour intensive solution to this one.

In making a Beamer presentation, I have some framed minipages with various arbitrary content I am transferring from a document to slides. I have some long minipages I'd like to be split such that they span across two or more single-column slides (preserving the frame box). I, of course could split up the minipages manually to smaller ones or play with fonts in some cases such that they fit into slides, but it's a tedious process. I'd rather automate, like Beamer allows with allowframebreaks+listings for automatic multi-slide content, but for minipages instead.

MWE

\documentclass{beamer}
  \mode<presentation>
\usepackage{lipsum}
\begin{document}

\begin{frame}[allowframebreaks,fragile]
\frametitle{Need to span the minipage across slides}
\begin{itemize}
   \item Sometimes
   \item need to
   \item span the
   \item minipage across
   \item multiple slides.
\end{itemize}
\fbox{\begin{minipage}[b]{.95\textwidth}%
\small
\lipsum[1-5]
\normalsize
\end{minipage}}
\end{frame}
\end{document}

Answer 1

This is not possible with the minipage environment: it is an unbreakable box by its very nature.

Other solutions include mdframed and tcolorbox environments, but unfortunately the page-breaking capabilities of each of these are defeated by beamer and its allowframebreaks option.

But I'd like to suggest that you avoid the allowframebreaks option. Quoting the beamer manual:

The use of this option is evil. In a (good) presentation you prepare each slide carefully and think twice before putting something on a certain slide rather than on some different slide. Using the allowframebreaks option invites the creation of horrible, endless presentations that resemble more a “paper projected on the wall” than a presentation. Nevertheless, the option does have its uses. Most noticeably, it can be convenient for automatically splitting bibliographies or long equations.

As mentioned in the last sentence: just about the only time I use allowframebreaks is for a reference/bibliography slide.

For a presentation, you should take the time to find natural breaking points so that things do not run on and on. Presumably you'll also be removing large chunks of content during the process of conversion (to avoid the dreaded wall-of-text slides), so you can treat the work of finding good frame breaks as a part of that task.

\documentclass{beamer}
  \mode<presentation>
\usepackage{lipsum}

\begin{document}
\begin{frame}
\frametitle{Need to span the minipage across slides}
\begin{itemize}
   \item Sometimes
   \item need to
   \item span the
   \item minipage across
   \item multiple slides.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{New frame I}
\fbox{\begin{minipage}[b]{.95\textwidth}%
\small
\lipsum[1]
\end{minipage}}
\end{frame}
\begin{frame}
\frametitle{New frame II}
\fbox{\begin{minipage}[b]{.95\textwidth}%
\lipsum[2]
\end{minipage}}
\end{frame}
\begin{frame}
\frametitle{New frame III}
\fbox{\begin{minipage}[b]{.95\textwidth}%
\small
\lipsum[3]
\end{minipage}}
\end{frame}
\end{document}

For contents that are close to fitting on a single frame, you can use the frame option shrink to fit them. But I only use this as an extreme last resort.