\ContinuedFloat from subfig package does it.
It sometimes occurs, especially when using sub-floats, that a single figure needs to be continued across pages. The \ContinuedFloat command is placed at the beginning of the floating environment or after changing @captype inside the floating environment to make the next figure, table or other floating \caption a continuation of the last float \caption of the same type. It does this by saving the sub-float numbering internally and keeping the float numbering from advancing.
Update:
The MWE is basically:
\begin{figure}
\subfloat[][]{A}
\subfloat[][]{B}
\caption{Fig. 1}
\end{figure}
\begin{figure}
\ContinuedFloat
\subfloat[][]{C}
\subfloat[][]{D}
\caption{Fig. 2}
\end{figure}
The production code looks like this, there is a lot of fiddling which I do not remember why it was done. It includes some fiddling with the figure counter to keep the same figure number.
\begin{figure}[pt]
\let\tabsepbakup\tabcolsep
\renewcommand{\tabcolsep}{0.1ex}
\begin{tabular}{rl}
\multicolumn{2}{r}{%
\sidebysidecaption{0.75\linewidth}{0.23\linewidth}{%
\subfloat[R1: The first section]{\begin{tabular}[b]{c}
\includegraphics[width=0.495\linewidth]{R1_scan.png}
\\
\includegraphics[width=0.495\linewidth]{scale.png}
\end{tabular}
\label{fig:km-4-a}}
%\hspace*{0.1ex}
\setcounter{subfigure}{3}%
\subfloat[R2: The first section]{\begin{tabular}[b]{c}
\includegraphics[width=0.495\linewidth]{R2_scan.png}
\\
\includegraphics[width=0.495\linewidth]{scale.png}
\end{tabular}
\label{fig:km-4-d}}
}{% \vspace*{1em}
\hspace*{\tabcolsep}\hspace*{0.1\linewidth}\vspace*{0pt}%
\hfill%
\caption[Regions of interest as sections and as reconstructions]{First scan of R1, R2
immunostaining in combination with front views of the 3D models
coloured for shape diameter and connectivity visualisation. Scale
bar for all images~$=$ \SI{200}{\micro\meter}. \emph{(Continued on the next page, full caption on page~\pageref{fig:km-4-caption}.)}}%
\label{fig:km-4}
}}
%
\setcounter{subfigure}{2} \\
\setcounter{subfigure}{1}%
\subfloat[R1: The shape diameter]{\includegraphics[width=0.495\linewidth]{r1_red_frame_br_.png}\label{fig:km-4-b}} &
\setcounter{subfigure}{4}%
\subfloat[R2: The shape diameter]{\includegraphics[width=0.495\linewidth]{r2_red-from_blue_y_bg.png}\label{fig:km-4-e}}
\\
\setcounter{subfigure}{2}%
\subfloat[R1: The connectivity study]{\includegraphics[width=0.495\linewidth]{r1_overview_frame_y_.png}\label{fig:km-4-c}} &
\setcounter{subfigure}{5}%
\subfloat[R2: The connectivity study]{\includegraphics[width=0.495\linewidth]{r2_overview_frame_y-border.png}\label{fig:km-4-f}} \\
\end{tabular}
\renewcommand{\tabcolsep}{\tabsepbakup}
%%% need a hack for contcaption
%%% increment the figure counter so it might be decremented again
\stepcounter{figure}
\end{figure}
\begin{figure}[tp]
\ContinuedFloat
%% <-------------------- that's the point
\let\tabsepbakup\tabcolsep
\renewcommand{\tabcolsep}{0.1ex}
\begin{tabular}{rl}
\multicolumn{2}{r}{%
\sidebysidecaption{0.24\linewidth}{0.75\linewidth}{%
\contcaption{\emph{(Continued from previous page.)} First scan of R3, R4
immunostaining and front views of the 3D models
coloured for shape diameter and connectivity visualisation. % Scale
% bar for all images~$=$ \SI{200}{\micro\meter}.
\emph{(Full caption on the next page.)}}
}{%
\hspace*{0pt}%
\vspace*{0pt}%
\hspace*{-0.5\linewidth}%
\hfill%
\subfloat[R3: The first section]{%
\renewcommand{\tabcolsep}{0ex}
\begin{tabular}[b]{c}
\includegraphics[height=0.495\linewidth]{R3_scan.png}
\\
\includegraphics[width=0.495\linewidth]{scale.png}\label{fig:km-4-g}
\end{tabular}%
\renewcommand{\tabcolsep}{0.1ex}
}%
\setcounter{subfigure}{9}%
\subfloat[R4: The first section]{%
\renewcommand{\tabcolsep}{0ex}
\begin{tabular}[b]{c}
\includegraphics[height=0.495\linewidth]{R4_scan.png}
\\
\includegraphics[width=0.495\linewidth]{scale.png}\label{fig:km-4-j}
\end{tabular}%
\renewcommand{\tabcolsep}{0.1ex}
}%
}\setcounter{subfigure}{7}}
\\
\subfloat[R3: The shape diameter]{\includegraphics[width=0.495\linewidth]{r3_red_frame_.png}\label{fig:km-4-h}} &
\setcounter{subfigure}{10}%
\subfloat[R4: The shape diameter]{\includegraphics[width=0.495\linewidth]{r4_red_frame_.png}\label{fig:km-4-i}}
\\
\setcounter{subfigure}{8}%
\subfloat[R3: The connectivity study]{\includegraphics[width=0.495\linewidth]{r3_blue_.png}\label{fig:km-4-k}}
&
\setcounter{subfigure}{11}%
\subfloat[R4: The connectivity study]{\includegraphics[width=0.495\linewidth]{r4_overview_front_.png}\label{fig:km-4-l}}
\\
\end{tabular}
\renewcommand{\tabcolsep}{\tabsepbakup}
\end{figure}
\begin{figure}[th]
\contcaption{\emph{(On two previous pages)} First scan of R1 (a), R2 (d), R3 (g) and R4 (j)
immunostaining in combination with front views of the 3D models
coloured for shape diameter (b, e, h, k) and connectivity visualisation
(c, f, i, l). In (b), (e), (h), and (k) a shape diameter below \SI{20}{\micro\meter} is
depicted in red and above \SI{40}{\micro\meter} in green. A transition from red to
green occurs in microvessels of shape diameters from \SI{20}{\micro\meter} to \SI{40}{\micro\meter} with middle at \SI{23.5}{\micro\meter}.
In (c), (i), and (l) the largest continuous microvessel network is depicted in light blue and all smaller networks are green. In (f)
there are several large networks, all coloured in blue. Small
structures sized between \SI{50}{\micro\meter} and \SI{12.5}{\micro\meter} are red in (c), (f), (i), and
(l), and all structures with a diameter less than \SI{12.5}{\micro\meter} in any
dimension are omitted. (b, c) R1; (e, f) R2; (h, i) R3; (k, l) R4. Scale
bar for all images: \SI{200}{\micro\meter}.}
\label{fig:km-4-caption}
\end{figure}
The \sidebysidecaption macro is not really related, but for the sake of completeness:
\newcommand{\sidebysidecaption}[4]{%
\RaggedRight%
% https://tex.stackexchange.com/questions/29143/caption-on-the-side-of-a-figure
\begin{minipage}[t]{#1}
\vspace*{0pt}
#3
\end{minipage}
% \mbox{}\\[-\baselineskip]
\hfill%
\begin{minipage}[t]{#2}
\vspace*{0pt}
#4
\end{minipage}%
% \mbox{}\\[-\baselineskip]
}
The production code above requires:
\usepackage[font=footnotesize,labelfont=sf,textfont=sf]{subfig}
\usepackage[footnotes]{ragged2e} % for RaggedRight
%% it is used with microtype
%% http://tex.stackexchange.com/questions/134303/does-combining-microtype-with-ragged-right-make-any-sense
\setlength\RaggedRightRightskip{1pt plus 2em minus 1pt} % default is: 0pt plus 2em
The final result looks like this:

.....(cont.)at the second caption or first caption? – aan Jan 01 '20 at 10:10bin\begin{subfigure}[b]{0.6\textwidth}) besideb,t? Is there a list to check all the options? – aan Jan 01 '20 at 11:49bmeaning in\begin{subfigure}[b]{0.6\textwidth}). – aan Jan 01 '20 at 12:50[b]are aligned at of images. With [t] option are aligned at the their top. In your case you can omit positioning options since sub-images are in vertical sequence, see edited answer – Zarko Jan 01 '20 at 14:11