2

I have to comply with inflexible publisher requirements. Both "Parts" and "Chapters" need to start on the same page, with the Chapter directly following the Part:

A. Part name

1. Chapter name

There should be no empty pages and Parts may start on both even and uneven pages.

I highly appreciate your support - I could not find any solution thru Google.

\documentclass{scrbook}
\begin{document}
\part{Foo}
\chapter{Bar}
text starts here
\end{document} 
2

Maybe the following helps:

\documentclass[
  open=any% start parts and chapters on both even and odd pages
  ]{scrbook}

\RedeclareSectionCommand[
  beforeskip=\dimexpr-3.3\baselineskip-\parskip\relax,
  afterskip=\dimexpr3.3\baselineskip+\parskip\relax,
  style=chapter% no part page
]{part}
\renewcommand\partformat{\partname\ \thepart\autodot\enskip}

\DeclareNewSectionCommand[
  beforeskip=-1sp,
  afterskip=1.725\baselineskip plus .115\baselineskip minus .192\baselineskip,
  style=section,% no page break before \firstchapterinpart
  level=\chapternumdepth,
  indent=0pt,
  tocindent=0pt,
  tocnumwidth=1.5em,
  font=\usekomafont{chapter},
  tocstyle=chapter
]{firstchapterinpart}

\makeatletter
\let\c@firstchapterinpart\c@chapter% use the same counter for both chapter and firstchapterinpart
\def\cl@firstchapterinpart{\cl@chapter}% use the same reset list as chapter
\makeatother

\begin{document}
\tableofcontents
\part{Foo}
\firstchapterinpart{Bar}
text starts here
\chapter{Next}
\end{document}

enter image description here

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