Beamer frame with page breaks and pause?

Question

I have a beamer frame which for some reasons I want to be with the allowframebreaks option (to have the frame title counter). I have multiple theorem boxes and a tikZ picture (inside a figure environment) on this frame, which spread over 2 pages. Now comes the fun part: I want to add \pause between some of the content to reveal it bit by bit, but this seems to mess it up, which I kind of understand, since it's technically still only one frame showing on multiple slides from the frame break and the pause at the same time... Does anyone have a better idea how to do this, or can tell me if this is even possible? Thanks heaps F

\documentclass{beamer}
\usetheme{CambridgeUS}
\usecolortheme{seahorse}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{csquotes}
\usepackage{graphicx}
\usepackage{pgfplots}
\setbeamertemplate{theorems}[ams style]
\begin{document}
\begin{frame}[allowframebreaks]{Theorems}
    \begin{theorem}
        Suppose $|I|\geq3$ and $\Theta$ is \textbf{rich}:\\
        For any $i,~\theta'_i,~\theta_i$, manipulation $\theta'_i$ is an \textbf{OM} for $\theta_i$ under mechanism $\phi\iff$ for any mechanism $\psi$ \textbf{i-undistinguishable} from $\phi,~\theta'_i$ is a \textbf{profitable} manipulation for $\theta_i$
    \end{theorem}
    %\pause
    \begin{figure}
        \centering
        \scalebox{.75}{\input{Plot1.tex}} %see my previous question
        %\caption{}
        %\label{fig:f1}
    \end{figure}
    %\pause
    \begin{theorem}
        Any stable-dominating mechanism is \textbf{not obviously manipulable}
    \end{theorem}
    %\pause
    \begin{theorem}
        Any stable mechanism is individually rational, Pareto efficient, and \textbf{not obviously manipulable}
    \end{theorem}
    %\pause
    \begin{theorem}
        The $(K+1)$-price auction is \textbf{not obviously manipulable}
    \end{theorem}
    %\pause
    \begin{theorem}
        Every efficient, individually rational, and weakly budget balanced mechanism is \textbf{obviously manipulable}
    \end{theorem}
\end{frame}
\end{document}

Answer 1

To quote from the beamer user guide:

You can use the option allowframebreaks to cause the ⟨frame text⟩ to be split among several slides, though you cannot use overlays then. (See p. 59)

and:

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 a consequence, I'd manually split the contents into 3 slides as follows:

\documentclass{beamer}
\usetheme{CambridgeUS}
\usecolortheme{seahorse}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{csquotes}
\usepackage{graphicx}
\usepackage{pgfplots}
\setbeamertemplate{theorems}[ams style]
\begin{document}
\begin{frame}{Theorems I}
    \begin{theorem}
        Suppose $|I|\geq3$ and $\Theta$ is \textbf{rich}:\\
        For any $i,~\theta'_i,~\theta_i$, manipulation $\theta'_i$ is an \textbf{OM} for $\theta_i$ under mechanism $\phi\iff$ for any mechanism $\psi$ \textbf{i-undistinguishable} from $\phi,~\theta'_i$ is a \textbf{profitable} manipulation for $\theta_i$
    \end{theorem}
\end{frame}
\begin{frame}{Theorems II}
    \begin{figure}
        \centering
        \scalebox{.75}{\input{Plot1.tex}} %see my previous question
        %\caption{}
        %\label{fig:f1}
    \end{figure}
\end{frame}
\begin{frame}{Theorem III}
    \begin{theorem}
        Any stable-dominating mechanism is \textbf{not obviously manipulable}
    \end{theorem}
    \pause
    \begin{theorem}
        Any stable mechanism is individually rational, Pareto efficient, and \textbf{not obviously manipulable}
    \end{theorem}
    \pause
    \begin{theorem}
        The $(K+1)$-price auction is \textbf{not obviously manipulable}
    \end{theorem}
    \pause
    \begin{theorem}
        Every efficient, individually rational, and weakly budget balanced mechanism is \textbf{obviously manipulable}
    \end{theorem}
\end{frame}
\end{document}