  This article revisits the problem of global well-posedness for the
generalized parabolic Anderson model on $\mathbb{R}^+\times \mathbb{T}^2$
within the framework of paracontrolled calculus \cite{GIP15}. The model is
given by the equation:
  \begin{equation*}
  (\partial_t-\Delta) u=F(u)\eta
  \end{equation*}
  where $\eta\in C^{-1-\kappa}$ with $1/6>\kappa>0$, and $F\in
C_b^2(\mathbb{R})$. Assume that $\eta\in C^{-1-\kappa}$ and can be lifted to
enhanced noise, we derive new a priori bounds. The key idea follows from the
recent work
  \cite{CFW24} by A.Chandra, G.L. Feltes and H.Weber to represent the leading
error term as a transport type term, and our techniques encompass the
paracontrolled calculus, the maximum principle, and the localization approach
(i.e. high-low frequency argument).
