Splitting the denominator of fraction into more than two lines

I wish to split the denominator of the following fraction into more than 2 lines. For splitting into two lines, splitfraccan be used. But how to split the denominator into three lines?

\documentclass{article}  \usepackage{mathtools}\begin{document}\begin{equation}\label{eq31} G_2(s) = \frac{K_pcT_rs+K_p}{\splitfrac{T_pT_rT_pT_ts^4 + \left(T_gT_pT_t + T_gT_pT_r + T_pT_tT_r + T_gT_rT_t\right)s^3}{ +  \left(T_pT_g + T_tT_g + T_rT_g + T_tT_p + T_rT_p +     T_rT_t\right)s^2+\left(T_g + T_r + T_t + T_p\right)s + 1 }}   \end{equation}    \end{document}