Printing two bibliographies using revtex4 template

Question

I'm writing a paper using the revtex4 to be submitted to the arxiv. It is for the Physical Review Letters journal. I want to include a bibliography section at the end of the main text, and another bibliography at the end of the supplementary information section. The suggestions in Printing the bibliography twice? are not helpful.

My MWE gives me errors saying there are package incompatibilities between biblatex and natbib (which is what I assume that revtex4 uses). Any suggestions would be great.

\pdfoutput=1
\documentclass[prl,twocolumn,floatfix,showpacs,superscriptaddress]{revtex4}
\usepackage{blindtext,lipsum}
%\usepackage{multibib}
%\usepackage{natbib}
\usepackage[backend=biber]{biblatex}
\addbibresource{mybib.bib}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amssymb}
\begin{document}
\title{my paper title}
\author{author 1}
\address{university 1}
\author{author 2}%
\address{university 2}
\date{\today}
\begin{abstract}
abstract of my paper
\end{abstract}
%\pacs{}
\maketitle
%% start main
\paragraph*{Introduction} -- This is my paper \cite{paper2007} \cite{paper2012}.
\lipsum[1-1]
\lipsum[2-4]
\paragraph*{References}
\printbibliography
\clearpage
\textbf{\large Supplementary Material}
%%%%%%%%%% Prefix a "S" to all equations, figures, tables and reset the counter %%%%%%%%%%
\setcounter{equation}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{page}{1}
\renewcommand{\theequation}{S\arabic{equation}}
\renewcommand{\thefigure}{S\arabic{figure}}
\renewcommand{\bibnumfmt}[1]{[S#1]}
\renewcommand{\citenumfont}[1]{S#1}
This Supplementary Material presents technical details \cite{paper2007} \cite{paper2010}...
\blindtext
\paragraph*{References}
\printbibliography
\end{document}