Using vertical multiline braces to denote difference as opposed to grouping

this is a hack, and a rather ridiculous one at that, but it was fun.

\documentclass[12pt]{article}

\begin{document}

\noindent
\hspace*{2em}Line 1\\
\smash{\makebox[2em]{\hfil\raisebox{.6\baselineskip}{$\alpha\,\big\{$}}}%
Line 2\\
\smash{\makebox[2em]{\hfil\raisebox{.6\baselineskip}{$\beta\,\big\{$}}}%
Line 3\\
\smash{\makebox[2em]{\hfil\raisebox{.6\baselineskip}{$\gamma\,\big\{$}}}%
Line 4

\end{document}