How to create Multilevel Colored Boxes using tcolorbox/any other package?

tcolorbox doesn't provide code to add more than one lower part. But you could add additional lines:

\documentclass{report}

\usepackage{tikz,tcolorbox}

\makeatletter
\newcommand{\DrawLine}{%
  \begin{tikzpicture}
  \path[use as bounding box] (0,0) -- (\linewidth,0);
  \draw[color=red!75!black,dashed,dash phase=2pt]
        (0-\kvtcb@leftlower-\kvtcb@boxsep,0)--
        (\linewidth+\kvtcb@rightlower+\kvtcb@boxsep,0);
  \end{tikzpicture}%
  }
\makeatother

\begin{document}

\begin{tcolorbox}[colback=red!5,colframe=red!75!black,title=My nice heading]

This is another \textbf{tcolorbox}.

\tcblower

Here, you see the lower part of the box.

\DrawLine

and some more

\end{tcolorbox}

\end{document}

This yields:

And here's one possibility using mdframed:

\documentclass{article}
\usepackage{xcolor}
\usepackage[framemethod=tikz]{mdframed}

\definecolor{mybrown}{RGB}{128,64,0}

\mdfdefinestyle{mystyle}{%
linecolor=mybrown,outerlinewidth=1pt,%
frametitlerule=true,frametitlefont=\sffamily\bfseries\color{white},%
frametitlerulewidth=1pt,frametitlerulecolor=mybrown,%
frametitlebackgroundcolor=mybrown,
backgroundcolor=mybrown!05,
innertopmargin=\topskip,
roundcorner=5pt
}
\mdtheorem[style=mystyle]{example}{Example}

\gdef\Sepline{%
  \par\noindent\makebox[\linewidth][l]{%
  \hspace*{-\mdflength{innerleftmargin}}%
   \tikz\draw[thick,dashed,gray!60] (0,0) --%
        (\textwidth+\the\mdflength{innerleftmargin}+\the\mdflength{innerrightmargin},0);
  }\par\nobreak}


\begin{document}

\begin{example}[The Title]
The contents of the first part.
\Sepline
\noindent The contents of the second part.
\Sepline
\noindent The contents of the third part.
\Sepline
\noindent The contents of the fourth part.
\end{example}

\end{document}

Here's now a modification not using a theorem-like structure, but a simple environment with a mandatory argument to provide a title:

\documentclass{article}
\usepackage{xcolor}
\usepackage[framemethod=tikz]{mdframed}

\definecolor{mybrown}{RGB}{128,64,0}

\mdfdefinestyle{mystyle}{%
linecolor=mybrown,outerlinewidth=1pt,%
frametitlerule=true,frametitlefont=\sffamily\bfseries\color{white},%
frametitlerulewidth=1pt,frametitlerulecolor=mybrown,%
frametitlebackgroundcolor=mybrown,
backgroundcolor=mybrown!05,
innertopmargin=\topskip,
roundcorner=5pt
}
\newmdenv[style=mystyle]{exa}
\newenvironment{example}[1]
  {\begin{exa}[frametitle=#1]}
  {\end{exa}}

\gdef\Sepline{%
  \par\noindent\makebox[\linewidth][l]{%
  \hspace*{-\mdflength{innerleftmargin}}%
   \tikz\draw[thick,dashed,gray!60] (0,0) --%
        (\textwidth+\the\mdflength{innerleftmargin}+\the\mdflength{innerrightmargin},0);
  }\par\nobreak}

\begin{document}

\begin{example}{The Title}
The contents of the first part.
\Sepline
\noindent The contents of the second part.
\Sepline
\noindent The contents of the third part.
\Sepline
\noindent The contents of the fourth part.
\end{example}

\end{document}